wide area signals based damping controllers for
TRANSCRIPT
Clemson UniversityTigerPrints
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5-2016
Wide Area Signals Based Damping Controllers forMultimachine Power SystemsKe TangClemson University, [email protected]
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Recommended CitationTang, Ke, "Wide Area Signals Based Damping Controllers for Multimachine Power Systems" (2016). All Dissertations. 1628.https://tigerprints.clemson.edu/all_dissertations/1628
WIDE AREA SIGNALS BASED DAMPING CONTROLLERS FOR MULTIMACHINE POWER SYSTEMS
A Dissertation Presented to
the Graduate School of Clemson University
In Partial Fulfillment of the Requirements for the Degree
Doctor of Philosophy Electrical Engineering
byKe Tang
May 2016
Accepted by: Dr. Ganesh Kumar Venayagamoorthy, Committee Chair
Dr. Keith Corzine Dr. Rajendra Singh
Dr. Amy Apon
ii
ABSTRACT
Nowadays, electric power systems are stressed and pushed toward their stability
margins due to increasing load demand and growing penetration levels of renewable energy
sources such as wind and solar power. Due to insufficient damping in power systems,
oscillations are likely to arise during transient and dynamic conditions. To avoid
undesirable power system states such as tripping of transmission lines, generation sources,
and loads, eventually leading to cascaded outages and blackouts, intelligent coordinated
control of a power system and its elements, from a global and local perspective, is needed.
The research performed in this dissertation is focused on intelligent analysis and
coordinated control of a power system to damp oscillations and improve its stability. Wide
area signals based coordinated control of power systems with and without a wind farm and
energy storage systems is investigated. A data-driven method for power system
identification is developed to obtain system matrices that can aid in the design of local and
wide area signals based power system stabilizers. Modal analysis is performed to
characterize oscillation modes using data-driven models. Data-driven models are used to
identify the most appropriate wide-area signals to utilize as inputs to damping controller(s)
and generator(s) to receive supplementary control.
Virtual Generators (VGs) are developed using the phenomena of generator coherency
to effectively and efficiently control power system oscillations. VG based Power System
Stabilizers (VG-PSSs) are proposed for optimal damping of power system oscillations.
Herein, speed deviation of VGs is used to generate a supplementary coordinated control
iii
signal for an identified generator(s) of maximum controllability. The parameters of a VG-
PSS(s) are heuristically tuned to provide maximum system damping.
To overcome ‘fallouts’ and ‘switching’ in coherent generator groups during
transients, an adaptive inter-area oscillation damping controller is developed using the
concept of artificial immune systems – innate and adaptive immunity.
With increasing levels of electric vehicles (EVs) on the road, the potential of
SmartParks (a large number of EVs in parking lots) for improving power system stability
is investigated. Intelligent multi-functional control of SmartParks using fuzzy logic based
controllers are investigated for damping power system oscillations, regulating transmission
line power flows and bus voltages.
In summary, a number of approaches and suggestions for improving modern power
system stability have been presented in this dissertation.
iv
DEDICATION
I would like to express my deepest gratitude to my parents for their continued support,
and my advisor and committee members for the wisdom from their expertise and
experience. Besides, I would like to express my gratitude to all the current students in my
laboratory for their generous help during the accomplishment of my Ph. D dissertation.
v
ACKNOWLEDGEMENT
Firstly, I would like to thank my advisor Dr. G. Kumar Venayagamoorthy for his
assistance to carry out the research and for his support to write this thesis. This work could
not have been accomplished without his abundant knowledge, his academic profession and
his generous support. I would also like to thank you for your patience and dedication of
time. Additionally, I would like to thank Dr. Keith Corzine, Dr. Rajendra Singh and Dr.
Amy Apon for serving on my committee.
Second, I would like to thank my parents. None of my achievements would have been
accomplished without your love and support.
Besides, I would like to thank all the members of Dr. G. Kumar Venayagamoorthy’s
research group member, for all the support and encouragement I have received from them
during the course of this project.
I would like to thank the Real-Time Power and Intelligent Systems (RTPIS)
Laboratory (http://rtpis.org/) for providing the world-class equipment and an excellent
working environment to facilitate my research work.
Last but not least, I would like to acknowledge the National Science Foundation and
Duke Energy for providing the financial support. This work is supported by the National
Science Foundation contract/grant number 1312260 and 1232070, as well as the Duke
Energy Distinguished Professor Endowment Fund. The views and conclusions herein are
those of the author and not the National Science Foundation or Duke Energy.
vi
TABLE OF CONTENTS
Page
TITLE PAGE ................................................................................................................ ii
ABSTRACT .................................................................................................................. ii
DEDICATION ............................................................................................................. iv
ACKNOWLEDGEMENT .............................................................................................v
LIST OF TABLES .........................................................................................................x
CHAPTERS
I. INTRODUCTION ..................................................................................................1
1.1 Overview .......................................................................................................1
1.1.1 Power System Stability .................................................................................... 2
1.1.2 Power System Oscillations .............................................................................. 4
1.1.3 Generator Coherency ....................................................................................... 5
1.2 Benchmark Power Systems ...........................................................................6
1.2.1 IEEE 12-Bus power system ............................................................................. 6
1.2.2 IEEE 68-Bus power system ............................................................................. 7
1.3 Approaches toward smart power systems .....................................................8
1.3.1 Data-driven modeling of power system ........................................................... 9
1.3.2 Generator coherency analysis ......................................................................... 9
1.3.3 Coherency based power system stabilizers .................................................... 10
1.3.4 Wide area signals based adaptive power system staiblizers .......................... 10
1.4 Objectives of this dissertation .....................................................................11
1.5 Contributions of this dissertation ................................................................11
vii
Table of Contents (Continued) Page
1.6 Summary .....................................................................................................12
II. POWER SYSTEM OSCILLATIONS .................................................................13
2.1 Introduction .................................................................................................13
2.2 Power system oscillations and damping torque ..........................................13
2.3 Active power transfer and power system oscillations .................................15
2.4 Summary .....................................................................................................18
III. MODAL ANALYSIS FOR OSCILLATIONS ...................................................19
3.1 Introduction .................................................................................................19
3.2 Stochastic subspace identification ...............................................................20
3.2.1 Input and output signal based SSI .................................................................. 22
3.2.2 Output based SSI ........................................................................................... 24
3.3 Decision of system order .............................................................................25
3.4 Observability factor of oscillation modes ...................................................26
3.5 Controllability factor of oscillation modes ..................................................27
3.6 Modal analysis results for IEEE-68Bus system .........................................28
3.7 Summary .....................................................................................................30
IV. ROBUST POWER SYSTEM STABILIZERS ...................................................31
4.1 Introduction .................................................................................................31
4.2 Power system stabilizer development using linear matrix inequality .........32
4.3 Performance verification .............................................................................36
4.4 Summary .....................................................................................................39
V. COHERENCY ANALYSIS ................................................................................40
5.1 Introduction .................................................................................................40
5.2 Coherency analysis using hierarchical clustering .......................................41
viii
Table of Contents (Continued) Page
5.3 Coherency analysis using K-harmonic means clustering ............................45
5.3.1 Mathematical formulation .............................................................................. 45
5.3.2 Online coherency grouping techniques .......................................................... 47
5.3.3 Number of groups .......................................................................................... 48
5.4 Summary .....................................................................................................55
VI. COHERENCY BASED DAMPING CONTROLLER .......................................56
6.1 Introduction .................................................................................................56
6.2 Development of VG-PSS ............................................................................59
6.2.1 Modal analysis based on system matrices ..................................................... 59
6.2.2 Inter-area oscillation analysis ........................................................................ 60
6.2.3 Structure of VG-PSS ...................................................................................... 60
6.2.4 Determination of virtual generators ............................................................... 62
6.2.5 PSO for VG-PSS tuning ................................................................................ 64
6.2.6 PSO versus other design techniques .............................................................. 67
6.2.7 Time delay compensation .............................................................................. 67
6.3 Simulation results ........................................................................................68
6.4 Summary .....................................................................................................77
VII. ADAPTIVE DAMPING CONTROLLER ........................................................78
7.1 Introduction .................................................................................................78
7.2 Problem formulation ....................................................................................79
7.3 Artificial immune system ............................................................................79
7.3.1 Innate immunity ............................................................................................. 80
7.3.2 Adaptive immunity ........................................................................................ 80
7.4 AIS based oscillation damping controller ...................................................83
7.4.1 Innate damping controller .............................................................................. 83
7.4.2 Adaptive damping controller ......................................................................... 85
7.5 Performance evaluation of AIS controller ...................................................87
7.6 Summary .....................................................................................................94
ix
Table of Contents (Continued)
Page
VIII WIDE-AREA MEASUREMENT BASED MULTI-OBJECTIVE SMARTPARK CONTROLLERS FOR A POWER SYSTEM WITH A WIND FARM .............95
8.1 Introduction .................................................................................................95
8.2 Problem formulation ...................................................................................95
8.3 Power system with a wind farm and SmartParks ......................................100
8.3.1 12-BUS FACTS benchmark test power system ......................................... 100
8.3.2 Wind farm model ........................................................................................ 101
8.3.3 SmartPark model ........................................................................................ 101
8.4 Development of an intelligent multi-functional controller (IMFC) for SmartParks ..............................................................................................104
8.4.1 Tagaki-Sugeno fuzzy network (TSFN) ...................................................... 105
8.4.2 MVO based TSFN parameter tuning .......................................................... 107
8.4.3 Development of IMFC for SmartPark installation at Bus 6 ....................... 108
8.4.4 Development of IMFC for SmartPark installation at Bus 4 ....................... 109
8.4.5 Development of IMFC for SmartPark installation at Bus 4 and 6 .............. 110
8.5 Simulation results......................................................................................111
8.6 Summary ...................................................................................................122
IX. CONCLUSION.................................................................................................123
9.1 Introduction ...............................................................................................123
9.2 Research summary ....................................................................................123
9.3 Main conclusions .......................................................................................124
9.4 Suggestions for future research .................................................................126
9.5 Summary ...................................................................................................127
REFERENCES ..........................................................................................................130
BIOGRAPHY ............................................................................................................139
x
LIST OF TABLES
Table Page
Table 2.1 Oscillation frequencies and Damping ratios under multiple cases. .........18
Table 4.1 Designed Controllers ................................................................................35
Table 5.1 Coherent generator groups for the general case ........................................44
Table 5.2 The Process of KHMC in Finding Group Centers ....................................46
Table 5.3 Group Merging and Splitting ...................................................................49
Table 5.4 Offline Clustering Result ..........................................................................51
Table 5.5 Coherency Grouping Result for Case I ....................................................53
Table 5.6 Coherency Grouping Result for Case II ...................................................55
Table 6.1 The optimized parameters of the VG-PSS ...............................................68
Table 6.2 Settling time of generator speed deviations for the three case studies (in
seconds)...................................................................................................76
Table 7.1 Tuned stimulation and inhibition factors .................................................87
Table 7.2 Damping ratio for different modes under Case I – III ..............................94
Table 8.1 Damping ratios of speed deviation responses ........................................114
Table A.1 The reference of generator active power for VG-PSS design ..............128
Table A.2 The reference of generator active power development of adaptive wide
area signal based PSS............................................................................129
xi
LIST OF FIGURES
Figure Page
Figure 1.1 The categories of power system stability ................................................2
Figure 1.2 IEEE 12-Bus power system with a wind farm ........................................7
Figure 1.3 IEEE 68-Bus power system .....................................................................8
Figure 2.1 IEEE 68-Bus 16-machine system ...........................................................16
Figure 2.2 Speed deviations plots of G15 for different values of P .....................17
Figure 2.3 Damping ratio change with respect to active power transfer from NE to
NY. .......................................................................................................17
Figure 3.1 PRBS injection location, PRBS signal and speed response of generator
G10. ......................................................................................................22
Figure 3.2 Impulses responses of systems with different orders. ..........................26
Figure 3.3 Identified system modes for P =680MW. ...........................................28
Figure 3.4 The phasor plot of observability factors of G1 ~ G16 obtained through
PRBS injection. ....................................................................................29
Figure 3.5 The controllability factors of G1 ~ G16 obtained through PRBS injection.
..............................................................................................................29
Figure 4.1 IEEE 68-Bus 16-machine system of thirteen-PSS installations with fault
locations shown. ...................................................................................32
Figure 4.2 Structure of PSS. ..................................................................................33
Figure 4.3 The diagram of PSS design. ..................................................................33
xii
List of Figures (Continued)
Page
Figure 4.4 The LMI design problem. .....................................................................34
Figure 4.5. Speed deviation of generators for Case I with and without PSSs. ......37
List of Figures (Continued)
Figure 4.6 Speed deviation of generators for Case II with and without PSSs. .......38
Figure 5.1 IEEE 68-bus 16-machine power system. Coherent groups obtained using
offline clustering is shown as colored regions .....................................42
Figure 5.2 Dendrogram of generator coherency for Case A ...................................43
Figure 5.3 Dendrogram of generator coherency for Case B ...................................43
Figure 5.4 Dendrogram of generator coherency for Case C ..................................44
Figure 5.5 Speed responses of the sixteen generators in IEEE 68-Bus system .....51
Figure 5.6 Speed response of generators following fault at bus 1 ..........................52
Figure 5.7 Online coherent generator groups for a three phase short circuit fault at
bus 1 in Figure 5.1 ...............................................................................52
Figure 5.8 Speed response of generators following fault at bus 8 .........................54
Figure 5.9 Online coherent generator groups for a three phase short circuit fault 54
Figure 6.1 The diagram of the proposed control scheme with VG-PSS .................58
Figure 6.2 The overall flowchart of design approach ............................................59
Figure 6.3 The proposed structure of VG-PSS ......................................................61
Figure 6.4 PSO flowchart for VG-PSS parameters tuning algorithm. ...................66
xiii
List of Figures (Continued)
Page
Figure 6.5 Case Study I -- The speed deviations plots of selected generators with
VG-PSS on G9. ....................................................................................69
Figure 6.6 Case Study I -- The speed deviations plots of selected generators for
different sites of VG-PSS installations. ...............................................70
Figure 6.7 Case Study II.A -- The speed deviations plots of selected generators with
VG-PSS on G9. ....................................................................................71
Figure 6.8 Case Study II.A -- The speed deviations plots of selected generators for
different sites of VG-PSS installations. ...............................................72
Figure 6.9 Case Study II.B -- The speed deviations plots of selected generators with
VG-PSS on G9 under a new load condition ........................................73
Figure 6.10 Case Study III -- The speed deviations plots of selected generators with
VG-PSS on G9. ....................................................................................74
Figure 6.11 Case Study III -- The speed deviations plots of selected generators for
different sites of VG-PSS installations. ...............................................75
Figure 6.12 Impact of time delay for the speed responses at G9. ..........................77
Figure 7.1 A biological immune system ................................................................81
Figure 7.2 The schematic of the proposed AIS based control for a dynamic
system. .................................................................................................82
Figure 7.3 Flowchart illustrating the development of an AIS based damping
controller. .............................................................................................84
xiv
List of Figures (Continued)
Page
Figure 7.4 Diagram of the proposed innate controller scheme. .............................85
Figure 7.5 Schematic diagram of the AIS based controller. ..................................89
Figure 7.6 Speed responses of selected generators with local PSSs installation under
Case I. ..................................................................................................90
Figure 7.7 Speed responses of selected generators with local PSSs installation under
Case II. .................................................................................................91
Figure 7.8 Speed responses of selected generators with local PSSs installation under
Case III. ................................................................................................92
Figure 7.9 Deviation of parameters with time for all.............................................93
Figure 8.1 The overall diagram for the SmartPark control scheme .......................99
Figure 8.2 12-bus power system ..........................................................................100
Figure 8.3 Schematic circuit representation of a SmartPark ................................102
Figure 8.4 The inner control loop for SmartPark .................................................102
Figure 8.5 The structure of IMFCs .......................................................................106
Figure 8.6 The flowchart for development of IMFC ..........................................112
Figure 8.7 The speed deviations of G2 and G3 following a 100ms three phase fault
at Bus 6. .............................................................................................114
Figure 8.8 The active power flows on transmission lines following wind speed
changes. ..............................................................................................115
xv
List of Figures (Continued)
Page
Figure 8.9 The active power output of the SmartPark 1 for Case 1. (Under wind
speed of 12 m/s) .................................................................................116
Figure 8.10 The voltage profile of selected buses. ..............................................117
Figure 8.11 The active power flows on transmission lines following wind speed
changes. ..............................................................................................118
Figure 8.12 The active power and reactive output of the SmartPark for Case 2. .119
Figure 8.13 Power system measurements following a 100ms three phase fault at
Bus 6. .................................................................................................120
Figure 8.14 The active power flows on transmission lines following wind speed
changes. ..............................................................................................121
1
CHAPTER 1
INTRODUCTION
1.1 Overview
During power system operations, oscillations can be frequently observed as a result of lack of
damping torques. Generally, these oscillations are easy to arise following contingencies while the
power system is under critical operating conditions. Without proper measures of control,
oscillations may lead to serious consequences such as tripping of generators and transmission lines.
The oscillation modes can be generally categorized into local modes, intra-area modes and inter-
area modes in terms of the frequencies and the size of areas involved in the oscillations. Rise of
inter-area modes are largely due to heavy loading of crucial transmission lines [1].
In previous research, various control schemes have been suggested for oscillation damping
control [2-4]. Power System Stabilizers (PSS) that make use of local measurement to provide
supplementary control signals were developed for damping control. Lead-lag compensation,
robust controller design, as well as other schemes have be adopted for PSS design. However, the
use of local measurements contain limited information, and may not be effective for damping of
inter-area oscillations [5]; instead, with the prevailing of Phasor Measurement Unit (PMU)
installation in the power system, wide area measurements become available and can be used for
oscillation damping [6-7].
The concept of generator coherency is suggested based on the phenomenon that generators
tend to oscillate in coherent groups following contingencies [1]. Each group of coherent generators
can be equivalent to a Virtual Generator (VG) as a mathematical simplification of power system.
In this dissertation, the notion of a virtual generator is used to assist the design of oscillation
controllers that maintains to power system rotor-angle stability.
2
1.1.1 Power System Stability
The issue of stability becomes an increasing concern in the inter-connected modern power
systems. This concern is partly due to the fact that more generators are required to maintain
synchronism in a more complicated power system topology. Meanwhile, the integration of
intermittent renewable energy brings about more uncertainty to the transient behavior of the power
system. Loss of power system stability has huge social and economic impacts, as can be illustrated
by the example of 1997 North American blackout.
As indicated in Figure 1.1 [8], three aspects of power system stability are broadly considered
in engineering practices: rotor angle stability, frequency stability and voltage stability. The first
two have a close relationship with the active power generation and transmission, while the latter
is more closely related to the voltage profile and the load dynamics of the power system. Each of
these three aspects of stability can be further classified into subcategories in terms of the intensity
of disturbances and the length of time.
Figure 1.1 The categories of power system stability
3
The study of phase-angle stability can be categorized into first-swing stability and oscillatory
stability, which are affected by synchronizing torque and damping torque respectively. The focus
of this study is on the maintenance of phase angle oscillatory stability through intelligent control
schemes that increases the damping torque. Nevertheless, the consideration for voltage stability,
frequency stability and phase angle first swing stability cannot be ignored during verification of
control effectiveness.
Traditional studies of power system stability have yielded various approaches for the design
of Power System Stabilizers (PSS). The measurements of generator speeds, phase angles and/or
output active power can be used to generate a supplementary control signal injected at Automatic
Voltage Regulator (AVR). This approach resulted in a supplementary torque on the generator
motor with a phase that is in exactly the opposite phase of the generator speed during oscillation.
However, the presence of effective traditional damping schemes cannot exclude further studies of
power system stability, due to the following considerations.
The advent of new analytic mathematical tools as exemplified by modern robust control
theorem and toolboxes, artificial intelligence based algorithms (such as neural
networks and fuzzy logics) can be applied for power system analysis and controller
design.
The usage of PMUs makes wide area measurement available, and can assist in stability
analysis and control. With the PMUs working at much higher sampling frequencies
than the traditional SCADA system, detailed power system dynamics can be captured.
The FACTS devices and SmartParks can be deployed to participate in the stability
control schemes. With the fast switching frequencies, FACTS can respond to control
signals instantaneously to regulate the power flows in the power systems.
4
The integration of wind and solar power into the power system leads to different levels
of transmission line power flows and reactive power output of generators. Thus, more
advanced control schemes are required to make the power system resistant to critical
operating conditions.
The application of energy storage devices (such as SmartParks) can impact the active
and reactive power flow in the power systems, and thus can serve for power system
control purposes.
The desired power system is able to maintain stability in spite of the increased complexity,
uncertainty and stochasticity. Thus, it is desired that improved control schemes be applied to the
power systems using more android analytic tools. The prevention of losses from the consequences
caused by power system oscillation is not the sole purpose of this research. If stability margin is
improved using novel state-of-art technologies, the power system will be able to operate under
more volatile conditions, leading to the potential for integration of more renewable energy.
1.1.2 Power System Oscillations
With the development of society, the increase of power system load requires improved delivery
capability. Unfortunately, this is limited by the rate of power system facility construction. As a
consequence, more power lines are gradually pushed toward the operation limits. Hereby, the
occurrence of oscillations becomes more frequent; reports of large area outages are thus becoming
common. This necessitates the need for more detailed analysis of oscillation phenomenon.
In a power system, active and reactive power are delivered through the transmission and
distribution networks that connects the generation units with the load. The balance of active power
generation and consumption are related to the steady state of system frequencies as well as the
phase angle of generator rotor. As for a generator, the increase in the active power output caused
5
an increase in the leading phase angles. Thus, while subject to a disturbance that causes a change
of active power flow, the fluctuations of the phase angle will occur under the influence of
synchronizing torque and damping torque during the electrical-mechanical dynamics. This
disturbance can be either a change of load, a change of power transmission in a line, or an outage
in a bus. Due to the nonlinear dynamic characteristic of generators and the interconnectivity of
power system, the process of phase angle fluctuation will involve multiple generators and
transmission lines, causing oscillations in the generator speed in all generators and active power
transmission in all major lines. In this sense, the oscillation is no longer a local phenomenal, but
engages the whole power system.
1.1.3 Generator Coherency
An interesting phenomenon is the oscillation of generators in coherent groups. Taking all
generator speeds in a power system as the measurements and plotted in the same time-domain
graph, it can be seen that some groups of generators are swinging in the same cluster of curves
against other groups. In many cases, it can be observed that a dominant mode appears in the
generators speed deviations, while different groups generally oscillate in different phase in terms
of this mode. In the meanwhile, other oscillation modes may also exist; as a result, generators
oscillating in the same coherent group may also oscillate against each other (have different phase
angle) in the other oscillation modes. A brief description of the oscillation phenomenon can be
indicated as follows.
Oscillation is not a local phenomenon; instead, multiple machines are involved in the
power system oscillations that are linked electro-mechanically with the active power
flow in the network.
6
Generators tend to oscillate in coherent groups, while each group are generally
composed of generators that have small electrical distances with each other. In many
cases, the geological distribution of generators are closely related to generator
coherency.
Instead of swinging in a sinusoidal manner, the power system oscillations generally
includes multiple modes. Generators oscillating coherently with the same phase at one
frequency, may be swinging in an opposite phase at another frequency.
The types of contingencies that trigger the oscillations can largely impact the active
power flow in the power network, and in term, lead to variations in generator coherency.
1.2 Benchmark Power Systems
1.2.1 IEEE 12-Bus power system
As indicated in Figure 1.2, this test system includes four generators (G1 through G4).The
bus near G1 serves as slack bus. In this study, traditional synchronous generator model is applied0
for G1, G2 and G3; while a doubly fed induction generator (DFIG) is used for G4, which is
propelled by a wind farm. In this case, the fluctuation of wind speed has huge impacts toward the
power generation at Bus 6, and thus affects the active power flow in the power system. Bus 4 is
the load bus that has large consumption of active power [9].
7
Figure 1.2 IEEE 12-Bus power system with a wind farm
1.2.2 IEEE 68-Bus power system
As indicated in Figure 1.3, the IEEE 68-Bus power system is mainly composed of several
part: New England (NE), New York (NY), and three other smaller exterior power systems that can
be equivalent with three generators. Thus overall, this power system includes 16 generators that
produces active power at different levels. (i. e. G1 through G16). Three major transmission lines
serve as connection corridor from NE to NY. (i. e. Bus 1-2, Bus 8-9, Bus 1-27). G13 serves as the
slack bus that maintains the active power balance between generation and load.
8
Figure 1.3 IEEE 68-Bus power system
1.3 Approaches toward smart power systems
In order to address the issue of power system oscillation for stability maintenance, various
approaches are used in this research for damping control. Although previous approaches has shown
the effective of traditional damping control schemes, this study focuses on the newly emerged
challenges and tools that are encountered by the modern power systems.
In this study, the phenomenon of power system oscillations are graphically introduced and
explored. A modal analysis for oscillations is carried out to assist damping controller design.
Besides, the generator coherency is studied; and mathematical simplification of generator groups
as virtual generators are derived with analytic tools. Thereafter, coherency-based damping
controllers are proposed and tested; and they are further improved to adapt to various operation
Area 3
Area 5
G7
G6
G9
G4
G5
G3
G8 G1
G2G13
G12
G11
G10
G16
G15
G14
59
23
61
29
58
22
28
26
60
25
53
2
24
21
16
56
57
19
20
55
10
13
15
14
17
27
64
11
6
5459
5
4
18
3
8
1
47
48 40
62
30
9
37
65
64
36
34
38
35
33
6311
43
45
3950
51
52
68
67
49
46
42
41
31
66
Area 1 Area 2
Area 4
New England Test System New York Power System
44
32
Area 3
Area 5
G7
G6
G9
G4
G5
G3
G8 G1
G2G13
G12
G11
G10
G16
G15
G14
59
23
61
29
58
22
28
26
60
25
53
2
24
21
16
56
57
19
20
55
10
13
15
14
17
27
64
11
6
5459
5
4
18
3
8
1
47
48 40
62
30
9
37
65
64
36
34
38
35
33
6311
43
45
3950
51
52
68
67
49
46
42
41
31
66
Area 1 Area 2
Area 4
New England Test System New York Power System
44
32
12
7
9
conditions using intelligent algorithms. Finally, a scheme for maintaining stability is proposed for
a power system with renewable energy integration.
1.3.1 Data-driven modeling of power system
In traditional power system stability analysis, accurate models of generators and loads are
created in terms of differential equations. For instances, a 6-order model differential equation can
be set up for each generator; and the load can use either constant impedance model or dynamic
model of higher orders. Thereafter, the model of power system is based on a large set of differential
equations that consider the interaction of generators, loads and the network. However, this buildup
is subject to the parameter change of power system components. Besides, different power system
models need to be rebuilt with the change of system operating condition. The linearized model for
power system stationary stability analysis is generally expressed in the form of system matrices.
The order of matrices can generally be very high for the full model of power systems. However,
in engineering practices, it is not always necessary to have representation of all system states.
System reduction is frequently applied for the simplification of power system model. An
alternative approach is to model the power system with fully data driven approaches. In this study,
measurements are made in response to injection of disturbances at crucial power system
components, and mathematical tools are applied to deduce the system matrices from the inputs and
outputs, as detailed in later sections.
1.3.2 Generator coherency analysis
As introduced above, the generators coherency is subject to variation of operating conditions.
Thus, it is desired to classify generators into different groups in response to the measurements that
reflect power system operating conditions. In this study, the coherency of generators are analyzed
based on both online and offline clustering algorithms. Changes of operating conditions may take
10
place during power system operations, yet the clustering tools designed in this study will be able
to capture these changes. Therefore, each group is equivalent to a virtual generator. Despite of the
fact that details of local and intra-area dynamics are partly ignored in the formulation of the virtual
generators, the validity for this simplification is based on the control effectiveness that is shown
by the proposed controllers.
1.3.3 Coherency based power system stabilizers
On the basis of the power system coherency, this research suggests a wide area signal based
controller that makes use of virtual generator speeds for damping control. A Virtual Generator
based Power System Stabilizer (VG-PSS) is proposed. The introduction of virtual generator notion
avoids the necessity to deal with the dynamics of individual generators in a multi-machine power
system. Besides, the controller is able to perceive and handle all major modes of inter-area
oscillations in the power system.
1.3.4 Wide area signals based adaptive power system staiblizers
Adaptivity is introduced to the VG-PSS to address the impact of operating condition change
on its damping effectiveness. In this study, Artificial Immune System (AIS) is adopted to impose
a deviation to the VG-PSS parameters during power system transient responses to disturbances.
The presence of innate immunity and adaptive immunity of AIS [10] further improves the
effectiveness of VG-PSS.
1.3.5 SmartPark for multiple control functions
The commercial use of electrical vehicle leads to the prevailing construction of SmartParks.
The batteries of SmartParks can be utilized for temporary active power storage and thus serve as
a shock absorber for surging active power in the power systems; they can also be utilized as a
damping controller. Meanwhile, the SmartPark can also supply reactive power for voltage
11
regulations. Instead of focusing on each one of these three functionalities, this study realizes all of
them simultaneously and coordinately.
1.4 Objectives of this dissertation
The objectives of this dissertation research are as follows:
Carry out generator coherency analysis to obtain virtual generator models.
Develop new methods based on data-driven approaches to analysis power system
oscillations.
Identify appropriate wide signals to observe power system oscillations.
Identify generators where wide-area damping controllers have maximum
controllability.
Develop a wide area measurement based adaptive damping controller for better
damping effectiveness.
Apply SmartPark in a power system to realize the functionalities of damping
controller, active power regulator and voltage regulator concurrently.
1.5 Contributions of this dissertation
The following contributions have been made and reported this document.
Developed and implemented K-Harmonic Means Clustering algorithm for generator
coherency analysis [11].
Suggested a Stochastic Subspace Identification algorithm to obtain the system
matrices for power systems [12].
System matrices based modal analysis to select optimal signals to observe and control
power system oscillations [13].
12
Developed a Virtual Generator based Power System Stabilizer for optimal damping
effectiveness [13].
Used Artificial Immune System to implement a wide area measurement based
adaptive damping controller [14].
Applied Intelligent Multi-funtional Fuzzy Controller to realize the functionality of
SmartParks as damping controller, active power regulator and voltage regulator
concurrently. [15].
1.6 Summary
In modern power systems, the maintenance of stability is constantly becoming a challenge
due to increasing industry and customer load, as well as the renewable energy integrations.
Fortunately, the advancing technology provides various intelligent control schemes; and remote
measurements are becoming available with the installation of PMUs. Making advantage of many
analytic tools, this study uses various approaches to provide damping torque in order to mitigate
inter-area oscillations in the power systems. The conception of generator coherency is also used to
assist in the design of damping controllers.
13
CHAPTER 2
POWER SYSTEM OSCILLATIONS
2.1 Introduction
The rise of oscillations in the modern power systems are largely due to the contradiction of
increased power flows and the limited transmission capabilities that pushes the power system to
the stability margin. Besides, while the fast responding Automatic voltage regulator (AVR)
enhances first swing stability by increasing the synchronism torque, research has shown a negative
effect of AVR toward the damping torque.[16] These oscillations manifest themselves through
various measurements such as generator phase angle, speed deviations, bus voltages and tie line
power flow.[17] Without supplementary damping torque supply, the volatile active power
fluctuation may cause crucial transmission lines to be tripped, triggering more contingencies that
further worsen both first swing and oscillatory stability of the power system
Power system oscillations are largely impacted by the active power flow that links the
generators with the loads. Due to the nonlinearity of generator characteristics, as soon as a
contingency causes generators to deviate from previous steady state, the phase angle of some
generators may lose either first swing stability or oscillatory stability, depending on the
synchronizing or damping torque on the generator shaft.
2.2 Power system oscillations and damping torque
Let Te(s) denote the electrical torque on the generator shaft expressed in terms of frequency
domain, while δ(s) is the rotor angle of the generators. The relationship between Te(s) and δ(s)
expressed as (2.1) can be figured out with mathematical modeling of the generator and the control
systems.
14
Te(s) =H(s) δ(s) (2.1)
Under a fixed frequency, i.e. s = jω , we have:
Te(jωo) =H(jωo) δ(jωo) (2.2)
The three terms Te(jωo), H(jωo) and δ(jωo) can be regarded as three complex values. As a
consequence, Te(jωo) can be decomposed into two terms as expressed in (2.3).
Te(jωo) = Ts(jωo)+Td(jωo) (2.3)
in which Ts(jωo) is in phase with the phase angle δ(jωo), while Td(jωo) is in phase with the
generator speed 90 degree ahead of δ(jωo). The amplitude of Ts is closely related to the
synchronizing torque that maintains the first swing stability, while the amplitude of Td is
closely related to the damping torque that maintains the oscillatory stability. Several properties
of the power system oscillations are shown as follows:
When damping torque Td decreases, the generator tend to oscillate with smaller
damping ratio, thus it take longer time to reach steady state.
When the decrease of Td crosses zero, a component of electrical torque that is in
opposite phase with the generator speed is resulted. Thus, a negative damping torque
makes the oscillation unstable with the increasing amplitude through time.
The value of ωo is directly related to the oscillation frequency. For instance, significant
oscillation with angle frequency of ωo is always accompanied by a small value of Td(jωo)
at ωo.
The values of these two torques are under influence of the overall power system model
including generator model, active power transfer and control schemes applied to generators.
For instance, the change in the active power flow in the power system may lead to a change in
generator phase angle and the electrical torque simultaneously, causing the variation of
15
damping torque. The next section is an exploration of the relationship between the oscillations
and power system operating conditions.
2.3 Active power transfer and power system oscillations
The flow of active power transfer impacts phase-angle stability. Under the same loading
condition, increase of active power generation at some generators will cause reduction of generator
at other generators, especially the generator at the slack bus. Accordingly, power flow will change
in the power system networks leading to a different operating condition. The location of
generations and loads may have a large impact on the oscillations. Generally, oscillation becomes
obvious when the load center and generation center do not overlap, especially when some critical
transmission lines connecting two areas in the system become heavily loaded. The magnitude of
oscillation is impacted by the extent of imbalanced distribution of loads and generations.
Occasionally, active power generation in one area of power system may be unanimously increasing,
resulting in the increased power flow in critical transmission lines. Under such condition, it can be
observed that the system matrices also varies from the nominal operating condition, the
eigenvalues of certain modes may approach to the imaginary axis, causing the rise of oscillation.
A serious contingency such as three-phase fault may trigger power system to lose stability due to
amplifying oscillation amplitudes. Besides, the tripping of crucial transmission lines linking two
areas will also result in a weaker link between different power system parts. Since less passage
ways exist for the inter-area power flows, the two subsystems at the sides of transmission lines
will be less electromagnetically coherent; and not sufficient damping torque for inter-area
oscillation modes may be generated.
To study the relationship of power transfers and the oscillations, the IEEE 68-Bus 16-
Machine system (also referred to as the NE-NY system) is used as shown in Figure 2.1. NE and
16
NY are connected by three crucial transmission lines Bus 8-Bus 9, Bus 2-Bus 1, Bus 27-Bus 1,
thus inter-area oscillation between NE and NY can be observed.
Figure 2.1 IEEE 68-Bus 16-machine system
Under the base operating condition, the total power transfer from NE to NY (sum of power
flow on lines 8-9, lines 2-1 and line 27-1) is 560 MW. Increase in NE-NY power transfer, P, is
investigated for the emergence of inter-area oscillation(s). In case of an increased power transfer,
an increase of active power generation in amount of P is equally shared by generators G1~G9 in
NE system, while the same amount of reduction is equally shared by rest of the generators G10 ~
G16 in NE-NY system. Shown in Figure 2.2 is the plot of speed deviation responses of G15 under
different values of P post a six-cycle three-phase fault at Bus 31. Oscillation is prominent when
P reaches 600MW; it further increases as the value of P rises. By visual inspection of the curves
in Figure 2.2, it can be seen that the dominant oscillation is around 0.22 Hz, which is verified by
the plot of damping ratio change with respect to active power transfer from NE to NY shown in
Area 3
Area 5
G7
G6
G9
G4
G5
G3
G8 G1
G2G13
G12
G11
G10
G16
G15
G14
59
23
61
29
58
22
28
26
60
25
53
2
24
21
16
56
57
19
20
55
10
13
15
14
17
27
64
11
6
5459
5
4
18
3
8
1
47
48 40
62
30
9
37
65
64
36
34
38
35
33
6311
43
45
3950
51
52
68
67
49
46
42
41
31
66
Area 1 Area 2
Area 4New England Test System New York Power System
44
32
Area 3
Area 5
G7
G6
G9
G4
G5
G3
G8 G1
G2G13
G12
G11
G10
G16
G15
G14
59
23
61
29
58
22
28
26
60
25
53
2
24
21
16
56
57
19
20
55
10
13
15
14
17
27
64
11
6
5459
5
4
18
3
8
1
47
48 40
62
30
9
37
65
64
36
34
38
35
33
6311
43
45
3950
51
52
68
67
49
46
42
41
31
66
Area 1 Area 2
Area 4New England Test System New York Power System
44
32
12
7
Fault location Line disconnected
17
Figure 2.3, which is drawn using modal analysis elaborated in Chapter 3. As the value of P
changes, the damping ratio changes significantly as listed in Table 2.1.
Figure 2.2 Speed deviations plots of G15 for different values of P
Figure 2.3 Damping ratio change with respect to active power transfer from NE to NY.
0 5 10 15 20 25 30-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1x 10
-3
Times (seconds)
Speed d
evia
tions (
p.u
.)
0MW
600MW
630MW
650MW
680MW
-1000 -500 0 500-5
0
5
10
15
20
25
30
Power Transfer from NE to NY (MW)
Dam
pin
g R
atio (
%)
0.22 Hz
0.65 Hz
0.54 Hz
0.42 Hz
18
Table 2.1 Oscillation frequencies and Damping ratios under multiple cases.
(MW)P Mode frequency and corresponding damping ratio
600 0.2235Hz, 11.53%
630 0.225Hz, 9.16%
650 0.2233Hz, 7.63%
680 0.2173Hz, 4.74%
700 0.2239Hz, 2.04%
720 0.2112Hz, 1.05%
740 0.2034Hz, -0.70%
It can be seen through Figure 2.3 and Table 2.1 that the damping ratio of 0.22 Hz rapidly
decreases with the increase of active power transfer from NE to NY that pushes the transmission
lines linking these two areas to the limits. Chapter 3 will further show that this mode is the
oscillation of generators in NE oscillating against the generators in NY.
2.4 Summary
The power system oscillation arises due to lack of damping torque, which is largely affected
by different operating conditions. Typically in a power system where the transmission of a large
amount of active power between two large areas takes place, the decrease of damping torque tend
to result in a reduced damping ratio for oscillations. This can serve as a scenario of basic case for
the damping control design in later chapters.
19
CHAPTER 3
MODAL ANALYSIS FOR OSCILLATIONS
3.1 Introduction
As mentioned above, power system oscillations generally occur in multiple modes. Different
mode exhibit itself through a distinct oscillation frequency, damping ratio as well as a different set
of power system devices that are participated in oscillations. By implementation of modal analysis,
oscillation modes that lack sufficient damping torque can be identified.
Before the development of a damping controller, it is essential to study the oscillations
analytically. For instances, in order to select proper input and output signals for the controllers, it
is desired that the measurements that best reflects the oscillation in concern are used as the input,
while the output signal need to be applied to a power system device that most effectively impacts
the electromagnetic transients of that oscillation mode. In order to achieve this, modal analysis
serves as a powerful tool. Besides facilitating controller design, modal analysis also provides a
way to exam the efficacy of a controller.
Prior to analyze the modes engaged in oscillations, it is necessary to obtain a model for the
power system without detailed mathematical model of every component that captures the full
dynamics. Traditional modeling of the power system is through the combination of differential
equations for each the power system component. However, since the number of components is
exponentially increasing in the modern power system, the bottom-up modeling of every
component may not be practical for a large power system. Also, the power system matrices
obtained through this approach are be characterized with high orders, which includes large amount
of redundant information resulted from excessively delicate mathematical formulations. Besides,
the change operating conditions (including power flow, active power generation, network topology
20
as well as power system components in operation) also affect the power system model. Thus, it is
desired that the power system model is constructed with fully data-driven approaches. Hereby, the
concept of data-driven refers to the methodology to obtain the system model through analysis of
inputs and outputs data, without delving into details of the transient dynamics for each component.
Despite the nonlinearity of power systems, representation of power systems through linear
state space has been widely adopted for stability analysis and control based on two facts: first,
although individual generators can only be best modelled by nonlinear differential equations,
modal analysis based on the linearization of interconnected power system near a nominal operating
point can effectively uncover the characteristics of oscillation modes; second, although power
systems are subject to changes of operating conditions, these variations are comparatively small
comparing to the major systematic topology and generator parameters that remain unchanged; thus,
the modal analysis results can be well applied to a range of operating points. Studies presented in
references [18-22] include state-space representation of power systems.
In this chapter, a fully data-driven approach is used for power system identification and
modal analysis, which provides a guideline for damping controller design as well as for the
verification of damping effectiveness for later chapters.
3.2 Stochastic subspace identification
The general conceptions of system matrices are used to better describe the dynamics of
linearized model of power systems, as expressed in A,B,C,D in (3.1);
( 1) ( ) ( )( ) ( ) ( )
x k Ax k Bu ky k Cx k Du k
(3.1)
Where u(k),y(k) and x(k) represents the inputs, outputs and system states at the moment of k.
Stochastic Subspace Identification (SSI) is an effective mathematical tool to recognize a system
21
through the inputs and outputs. SSI algorithm regards the system matrices as the map from the past
data to future data. Generally, in order to design a PSS for stabilizing control, the supplementary
signal at the AVR of generators are regarded as the input and the speed deviation responses are
taken as the output. In this study, in order to identify the system dynamics, Pseudo-Random binary
signals are injected as the input signals to disturb the power system.
This is exemplified by an approach to identify generator G10 regarded as a Single Input
Single Output (SISO) system, as shown in Figure 3.1. In this approach, PRBS is injected at the
AVR of G10, while the speed deviation of G10 is measured as output. For other approaches,
multiple inputs and outputs can also be used. Figure 3.1(a) is the injection location of PRBS, vt
and vt_ref signify generator terminal voltage and its reference value. Figure 3.1(b) is the PRBS
waveform applied to generator G10, whose spectrum covers the frequency range of power system
oscillation (0.1Hz – 2 Hz). Figure 3.1(c) is the actual speed response of G10 plotted together with
expected speed response calculated through the linearized model of G1, indicating that the power
system fits to the linearized model with accuracy.
(a)
22
(b)
(c)
Figure 3.1 PRBS injection location, PRBS signal and speed response of generator G10.
(a) Structure block diagram of AVR showing PRBS injecting site; (b) PRBS signals;(c) speed responses and its estimated value at G10
Though previous research has used SSI for power system identification [23], it is not applied
for Multiple Input Multiple Output (MIMO) case; besides, the matrices B and C, were not
identified. In the following cases shown, SSI is applied to (a) an input/output based model and (b)
an output based model of the power system.
3.2.1 Input and output signal based SSI
In this case, the power system is modelled as a discrete system with the following expression:
1 1
1 1
( 1) ( ) ( )( ) ( ) ( )
x k A x k B u kk C x k D u k
(3.2)
0 10 20 30 40 50 60 70 80 90 100-0.02 -0.01
0 0.01
0.02
Time: (s)
Am
plit
ude
(p
. u.)
0 10 20 30 40 50 60 70 80 90 100-4
-2
0
2
4 x 10 -5
Time: (s)
Spee
d d
evia
tion
: (p
. u.)
Actual speed deviation Speed dev. of linearized model
23
in which the column vectors x, ω, u are the system states, supplementary inputs and speed
deviations respectively. k refers to the time step; in this case 0.064s is taken to be the gap between
each time step. A Hankel matrix of the past data array{u(k) | k = 0,1,…i+j-2} is defined as,
0| 1
0| 1
(0) (1) ... ( 1)(1) (2) ... ( )... ... ... ...
( 1) ( ) ... ( 2)
(0) (1) ... ( 1)(1) (2) ... ( )... ... ... ...
( 1) ( ) ... ( 2)
past i
past i
u u u ju u u j
U U
u i u i u i j
jj
Y Y
i i i j
(3.3)
A Hankel matrix of the future input data array {u(k) | k = i,i+1,…, 2i+j-2} is also defined as,
|2 1
|2 1
( ) ( 1) ... ( 1)( 1) ( 2) ... ( )... ... ... ...
(2 1) (2 ) ... (2 2)
( ) ( 1) ... ( 1)( 1) ( 2) ... ( )... ... ... ...
(2 1) (2 ) ... (2 2)
future i i
future i i
u i u i u i ju i u i u i j
U U
u i u i u i j
i i i ji i i j
Y Y
i i i j
(3.4)
Now, a historical data set is defined as,
[ , ]T T Tpast past pastW U Y (3.5)
It is easy to know from linear system theory that the future output Yfuture is impacted not only
by historic data set Wpast, but also by future inputs Ufuture. Thus, in order to figure out the map from
Wpast to Yfuture with the absence of Ufuture, an oblique projection from Yfuture to Wpast along Ufuture is
considered and is defined as,
24
/futurei future U pastO Y W (3.6)
Then singular value decomposition is applied as follows,
1 11 2
2
00 0
TT
i i iT
S VO USV U U G X
V
(3.7)
pinv( )i i iX G O (3.8)
where 1/21 1iG U S ; “pinv()” stands for the Moore-Penrose pseudo-inverse. It can be seen that each
column of Xi has the same dimension as the state variable x; it actually represents the estimation
of system states at each specific time. Xi+1 can be figured out in a similar way as Xi using (3.5) ~
(3.8) but replacing Upast, Ypast, Ufuture, Yfuture with 0|past iU U , 0|past iY Y , 1|2 1future i iU U , 1|2 1future i iU U
defined in a similar way as (3.3) ~ (3.4). Since the estimation of state variables at every specific
moment should satisfy (3.2), the system matrices A,B,C,D can be estimated from formulae (3.9)
by taking another pseudo-inverse,
1
| |
i i
i i i i
X XA BY UC D
(3.9)
Through this approach, the system matrices can be identified in two steps: (i) injection of PRBS
as the system input, and measure the system output; (ii) using formulae (3.2) ~ (3.9) to compute
system matrices.
3.2.2 Output based SSI
There are also some cases when it is not practical to inject PRBS to the power system as
supplementary inputs; instead, accurate modal analysis is required to be implemented only
according to the measured speed deviations, especially when a contingency happens. Different
25
from the previous case, the power system is equivalent with a discrete model where the input is
absent:
1
1
( 1) ( )( ) ( )
x k A x kk C x k
(3.10)
The computation process for Xi and Xi+1 is similar as the previous case except for that there
is no need to compute any values related to the input Upast and Ufuture; besides, Wpast should be
replaced with Ypast. Then, the matrices A and C can be calculated based on (3.11).
1
|
ii
i i
X AX
Y C
(3.11)
Through this approach, the system matrices can be identified in two steps: (i) following a
contingency in a power system, collect speed response deviations of all generators for a certain
window of time after the fault is tripped; (ii) compute system matrices based on a similar set of
formulae.
3.3 Decision of system order
Once the systematic matrices are obtained, the transfer function from input to output can be
decided and impulse response can be plotted. When system order is properly specified, the impulse
response will have minimal change as the system order further increases. By comparison of
impulse responses under different system orders, a correct value can be determined.
This is exemplified in Figure 3.2 for G10. Through SSI, impulse responses of a 3rd-, 4th-, 5th-
and 6th-order model are plotted together in the same diagram for comparison. A third order system
fails to catch up with system dynamics; nevertheless, it is evident that a 4th-order model is able to
represent the system, since impulse responses from 4th- or higher models appear to overlap.
26
Figure 3.2 Impulses responses of systems with different orders.
The identified system matrices for G10 are:
10
0.4439 0.6057 3.1296 0.96690.0467 0.1160 7.3734 0.11233.5372 7.8953 0.4947 2.2057
0.2754 0.0976 2.0730 0.0327
A
10 0.1863 0.0564 0.6314 0.0659 TB
10
910
0.0066 0.0037 0.0059 0.0046
2.0 10 0
C
D
Besides this example, another approach is to consider all the generator speed deviations as
the outputs, while all the AVR supplementary signals serve as the inputs. For any specific case,
other inputs and outputs can be chosen accordingly. Once the system matrices are identified, it is
of interest to figure out the existing oscillation modes. For each generator, the observability factor
of each mode needs to be calculated. Also, for each control input channel, the controllability factor
to each mode needs to be figured out.
3.4 Observability factor of oscillation modes
With the system matrix A, use singular value decomposition:
TA V W (3.12)
Time: (s)
Am
plit
ude
(p
. u
.)
3rd order
4th order
5th order
6th order
0 15
27
where TVW I and 1 2{ , ,... }ndiag ;
Each angular value σi is a representation of an oscillation mode. The corresponding
frequency of this mode is σi /2π. When the system order is set to be higher than the number of
actual oscillating modes, some of the modes embroiled in Λ will exhibit low connectivity with the
inputs and outputs.
Corresponding to the ith singular value σi, the observability factor of the mth input is
calculated as:
mi m ic v (3.13)
where cm is the mth row of matrix C, while iv is the ith column of matrix V. Since both of the two SSI
approaches can yield the matrix C, the observability factors can be calculated under both cases.
A high value of observability factor for a generator signifies that the measurements from this
generator has high component of that oscillation mode; and thus the measurements from this
generator can be selected as an input of damping controller.
3.5 Controllability factor of oscillation modes
Corresponding to σi, the controllability factor of the nth output is calculated as:
in i nw b (3.14)
where wi is the ith row of matrix W while bn is the mth column of matrix B. Since only the first SSI
approach can yield the matrix B, the controllability factors can be calculated only under the first
case.
A high value of controllability factor for a generator signifies that the AVR supplementary
signal has large impact toward this oscillation mode; and is suitable to be selected as an output of
damping controller.
28
3.6 Modal analysis results for IEEE-68Bus system
Using the approaches elaborated above, the PRBS signals are injected at the AVR of all
generators in IEEE 68-Bus power system under the power transfer from NE to NY of P =680MW.
The speed deviations of all the generators are measured. With these inputs and outputs, power
system matrices are identified. Using SVD for matrix A, major oscillation modes are identified
and shown in Figure 3.3.
Figure 3.3 Identified system modes for P =680MW.
It can be seen that the oscillation at 0.22Hz is a prominent and poorly damped mode. The
observability factors calculated by (3.13) are complex numbers and can thus be regarded as phasors.
For a specific oscillation mode, the observability factor phasors of all generators can be calculated
and plotted. The directions of these phasors can partially reflect the coherency of generators
engaged in the oscillation mode. Shown in Figure 3.4 is the phasor plot of observability factor of
each generator at the mode of 0.22 Hz. This mode is roughly the oscillation of NE area against NY
area: G1~G9 are oscillating against G10~G16; this oscillation is especially prominent on G14,
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.9152Hz
4.31% 0.57747Hz
8.2627% 0.43732Hz
11.16%
0.2243Hz
4.87%
0.21478Hz
23.4358%
Frequency (Hz)
Resid
ue /
Dam
pin
g r
atio
Dominant Inter-area
weakly damped mode
29
G15, G16. Correspondingly, the controllability factors are shown in Figure 3.5. It can be seen that
G8 and G9 are the two generators with highest controllability factors.
Figure 3.4 The phasor plot of observability factors of G1 ~ G16 obtained through PRBS injection.
Figure 3.5 The controllability factors of G1 ~ G16 obtained through PRBS injection.
-6 -4 -2 0 2 4 6 8
x 10-3
-6
-4
-2
0
2
4
6x 10
-3
1 G2 G3
G4 G5 G6
G7
G8
G9 G10
G11
G12 G13
G14 G15
G16
Real Axis
Imagin
ary
Axis
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Conto
llabilt
y f
acto
r
Generator Index
30
It is noticed that the generators with highest observability factors are different from those
with highest controllability, which is very common in many cases of inter-area oscillations. In
another words, the speed deviation of the generator most effective to implement damping control
may not be identical with the generator that the concerned oscillation mode can be observed. This
leads to the conclusion that local damping control is not sufficient for inter-area oscillations.
3.7 Summary
This chapter focuses on the methodology for modal analysis of the power system. First, an
SSI algorithm is applied to obtain the power system matrices following PRBS injections on AVRs
of all the generators to trigger power system transients. These matrices serve as a linearized power
system model that includes all the oscillation modes. Based on singular value decomposition, all
the oscillation modes can be identified and analysed. Besides, the observability and controllability
factors for all the generators can be calculated, which serves as a guidance for input and output
signal selection for damping controller design.
31
CHAPTER 4
ROBUST POWER SYSTEM STABILIZERS
4.1 Introduction
As power systems are operated close to the stability margin, oscillation caused by lack of
damping torque is frequently observed. Power System Stabilizer (PSS) enhances generator
stability by providing a supplementary signal to the automatic voltage regulator which enhances
the damping torque. Traditionally, PSSs are tuned by phase compensation of selected modes using
lead-lag compensators: the damping torque brought by PSS signals are expected to be exactly in
opposite phase with speed responses at the oscillation frequency. From perspective of control
theory, corresponding eigenvalues are shifted to the left in the complex plane. Based on this idea,
PSSs are designed after oscillation modes are obtained through Prony analysis in [4]. In [3], the
PSSs are regarded as filters for single modes during the design. However, since oscillations usually
occur in multiple modes, it is not guaranteed that all modes show reduced oscillation by such
design.
There are also applications of robust control schemes for PSS design. An H∞ design approach
is introduced in [24] to satisfy stability margin and disturbance attenuation requirements.
Elaborated in [25] is a dual-input PSS-design scheme using Glover-McFalane’s loop-shaping. In
[26], a mixed H2 /H∞ PSS design for a double-fed induction generator which shows robustness to
large disturbances is presented. Besides, PSSs can be designed through robust pole placement [27],
as well as conic programming [28]. Though there are abundant LMI tools to solve those robust
control problems, accurate linearized model is hard to obtain for an interconnected power system,
calling for data-driven approaches. Fortunately, this study makes use of the modal analysis
elaborated in the previous chapter: Stochastic Subspace Identification (SSI) algorithm is applied
32
to obtain a linearized single-input-multiple-output model of a power system and the Linear Matrix
Inequality (LMI) approach is then used to design several PSSs.
4.2 Power system stabilizer development using linear matrix inequality
In this study, PSSs are tuned in order to stabilize a multi-machine power system during
different disturbances. IEEE 68-Bus power system is used as shown in Figure 4.1, with the PSS
installation locations clearly marked. According to previous chapters, oscillation occurs in multiple
modes. Despite that geographically remote generators may swing in totally different frequency
range, local PSSs should be tuned to reduce the oscillation magnitude as well as the settling time.
Figure 4.1 IEEE 68-Bus 16-machine system of thirteen-PSS installations with fault locations shown.
Traditional PSS structure is shown in the upper part of Figure 4.2. It comprises a washout
filter, an amplitude limiter and a lead-lag compensator composed of two first-order functions
connected in series. This compensator can also be written in a more generalized 2nd-order transfer
function form as shown in the lower part of Figure 4.2, which is the standard structure adopted for
PSS in the industry today. Same parameters are used for the washout filters and limiters for all
33
PSSs. Thus for each of them, only the parameters in the 2nd-order transfer function need to be
figured out. The two-step PSS design process is shown in Figure 4.3. The processes inside the loop
are repeated to a number of PSSs one by one, for all generators in the system.
Figure 4.2 Structure of PSS.
Figure 4.3 The diagram of PSS design.
LMI is a mathematical tool that is useful in pole-placement and H2/H∞ control [29]. Using
the controlled system matrices, linear controller can be easily designed. Traditionally, controller
may take either output or state variable of the controlled system as input. In this study, since the
state variables are not observable, output-feedback instead of state-feedback controller is adopted,
as indicated in Figure 4.4. Letter u represents the controller output that is added to AVR
34
supplementary signal v. Given the continuous model matrices , , ,Mi Mi Mi MiA B C D , the open-loop power
system can be described as:
2
Mi Mi Mi
Mi Mi Mi
x A x B u B vy C x D u D vz uz y
(4.1)
Figure 4.4 The LMI design problem.
The aim is to design a controller with state space realization , , ,Ci Ci Ci CiA B C D to make the closed
loop transfer functions fromv to 2z and z satisfy:
Min 2 2z vT (4.2)
Subject to z vT
(4.3)
under the pole-placement requirement that every closed-loop pole i satisfies:
min ( ) 0ireal (4.4)
The order of controller equals that of the controlled system. The purpose of (4.2) is to minimize
speed deviation y subjected to a disturbance in v, so that the power system can be stabilized
following a contingency. Meanwhile, since it is not expected to have excessively large control
effort u, another constraint is set by (4.3). (4.1) ~ (4.4) have defined a mixed H2/H∞ output-
feedback design scheme that can be straightforwardly solved using MATLAB LMI toolbox [26].
A solution not may necessarily exist for every mathematical problem of this type, especially when
the controlled system has complex dynamics. Fortunately in this case, the power system model
obtained is of moderate order, leading to feasible design scheme.
35
Theoretically, the designed output-feedback controller can be replaced by an equivalent
transfer function; putting together with a washout filter and a magnitude limiter, a PSS can be
formed. However, it is not desired to have a PSS of high orders. Thus, after the controller is
designed and its matrices are known, it is further reduced to a 2nd-order transfer function through
balanced truncation. This process can also be implemented with MATLAB. Shown in Table 4.1
are the PSS controllers designed for thirteen generators.
Table 4.1 Designed Controllers
GeneratorIndex
System order Controller
G1 10 2
2
5.32 1110 34702.805 792.4
s ss s
G2 6 2
2
3.8365 34.94 1095818 345.9
s ss s
G3 10 2
2
12.26 176.3 212403.096 1752
s ss s
G4 10 2
2
33.88 636.6 125.939.96 3.558
s ss s
G5 12 2
2
39 766 513805.079 1889
s ss s
G6 12 2
2
27.4 1446 203402.708 646.7
s ss s
G7 8 2
2
24 31485 224102.969 1356
s ss s
G8 6 2
2
4.182 210.7 73832.706 642.9
s ss s
G9 8 2
2
0.5 54.25 10.834.243 2.538
s ss s
G10 4 2
2
28.77 87.5 1384.56.402 58.31
s ss s
G12 12 2
2
3.591 745.2 14102.503 337
s ss s
G13 8 2
2
2.836 46.11 320.111.45 45.44
s ss s
G14 6 2
2
55.15 761.8 487.22.773 101.9
s ss s
36
4.3 Performance verification
After the installation of all designed PSSs based on LMI-SSI approach described above, their
efficacy is examined through real-time simulation results carried out on the real-time digital
simulator (RTDS). Two cases corresponding to different contingencies and loading conditions are
considered during the simulations.
Case I: 8-cycle fault at Bus 2. Shown in Figure 4.5 is the comparison of speed deviation
responses with and without PSSs of the 13 generators with PSS installation.
Case II: 8-cycle fault at Bus 27, then the line connecting Bus 27 and Bus 1 is tripped.
Simulation result is shown in Figure 4.6.
It can be seen from these figures that with PSS installation, the power system settles to steady
state with quicker; meanwhile, the oscillation amplitude is also reduced. Though totally different
oscillation frequency may be observed for each generator following various contingencies, it can
be seen that the designed PSSs are able to stabilize the power system in both cases.
37
Figure 4.5. Speed deviation of generators for Case I with and without PSSs.
0 2 4 6 8 10 12-0.01
-0.005
0
0.005
0.01
G1
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-6
-4
-2
0
2
4x 10
-3 G2
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-8
-6
-4
-2
0
2
4x 10
-3 G3
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-0.01
-0.005
0
0.005
0.01
G4
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-0.01
-0.005
0
0.005
0.01
G5
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-0.01
-0.005
0
0.005
0.01
G6
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-0.01
-0.005
0
0.005
0.01
G7
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-0.01
-0.005
0
0.005
0.01
G9
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-4
-2
0
2
4x 10
-3 G10
Time: (s)S
pe
ed
de
v: (p
.u.)
0 2 4 6 8 10 12-4
-2
0
2
4x 10
-3 G12
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-4
-2
0
2
4x 10
-3 G13
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12-3
-2
-1
0
1
2
3x 10
-3 G14
Time: (s)
Sp
ee
d d
ev: (p
.u.)
Without PSSs
With PSSsSp
eed
dev.
in p
. u.
G1
Time: (s)
G2
Time : (s) Time: (s) G3
Time: (s)
G4
Time: (s)
G5
Time: (s)
G6
G8
G7
G12
G10
G13
G14
Time: (s)
Time: (s)
Time: (s)
Time: (s)
Time: (s)
Time: (s)
Time: (s)
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
. u.
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
. u.
Spee
d de
v. in
p. u
.
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
. u.
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
. u.
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
. u.
38
Figure 4.6 Speed deviation of generators for Case II with and without PSSs.
Without PSSs With PSSs
0 2 4 6 8 10 12 14 16 18 20-4
-3
-2
-1
0
1
2x 10
-3 G1
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-3
-2
-1
0
1
2
3x 10
-3 G2
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-3
-2
-1
0
1
2
3x 10
-3 G3
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-4
-2
0
2
4x 10
-3 G4
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-4
-2
0
2
4x 10
-3 G5
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-4
-2
0
2
4x 10
-3 G6
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-6
-4
-2
0
2
4x 10
-3 G7
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-8
-6
-4
-2
0
2
4x 10
-3 G9
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-1.5
-1
-0.5
0
0.5
1
1.5x 10
-3 G10
Time: (s)S
pe
ed
de
v: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-2
-1
0
1
2x 10
-3 G12
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-2
-1
0
1
2
3x 10
-3 G13
Time: (s)
Sp
ee
d d
ev: (p
.u.)
0 2 4 6 8 10 12 14 16 18 20-1.5
-1
-0.5
0
0.5
1
1.5x 10
-3 G14
Time: (s)
Sp
ee
d d
ev: (p
.u.)
With PSS
Spee
d de
v. in
p. u
.
G1
Time: (s)
G2
Time: (s)
G3
Time: (s)
G4
Time: (s)
G5
Time: (s)
G6
G8
G7
G12
G10
G13
G14
Time: (s)
Time: (s)
Time: (s)
Time: (s)
Time: (s)
Time: (s)
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
. u.
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
.u.
Spee
d de
v. in
p. u
.
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
. u.
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
.u.
Spee
d de
v. in
p. u
.Sp
eed
dev.
in p
. u.
Time: (s)
39
4.4 Summary
A new approach to tune PSS for multi-machine power system based on SSI and LMI
approach has been presented. Through analysis of system input and output data, SSI is able to
identify a single-input-multiple-output linearized power system and obtain its system matrices.
Thereafter, a LMI approach is applied to design an output-feedback controller that minimizes the
speed deviation response with limited control efforts. With subsequent order-reduction, the
designed controller can be implemented with a washout filter and a magnitude limiter to form the
standard PSS structure, typical case studies have shown that the LMI-SSI based PSS design is
effective for damping various modes of oscillation that exhibit in an interconnected multi-machine
power system.
40
CHAPTER 5
COHERENCY ANALYSIS
5.1 Introduction
Two factors make coherency analysis essential. In modeling and simulation of a power system that
includes large number of synchronous generators, as the size of grid expands, detailed transient analysis
becomes inhibiting due to significant calculation burden, leading to the requirement for a simplified model
to be obtained by generator clustering. Besides, Wide Area Control (WAC) is an effective way for
oscillation-damping control in order to maintain transient stability. Correct formulation of coherent groups
can provide virtual generator speed that can be used as WAC measurement signals.
It was traditionally regarded that the power system can be divided into several coherent areas where
generators in a given area tend to remain “in phase” in most cases. However, different events or
disturbances can affect the grouping results. For instance, an event happening near a coherent group may
cause its member generators to lose coherency during oscillation, as indicated in [1]. Thus, for effective
damping control for online operation of power systems, it is essential to have an online adaptive coherency
grouping approach.
The study on coherency analysis has been carried on for a very long time. With the speed deviation
data in time series from each generator, coherency analysis can be carried out, using either deterministic
or heuristic approaches, based on either the time-domain or frequency domain characteristics of the data.
Short-time Fourier analysis [2], Hilbert transform [30], Prony analysis [31] all serve as good alternatives.
Since approaches that focus on frequency domain characteristics are extremely time-consuming, time
domain based clustering is used for this study. Hereby, hierarchical clustering is a good approach by
consecutively merging small groups. Meanwhile, it is required that a faster and accurate clustering
41
algorithm be developed; thus, K-harmonic means clustering (KHMC) approach is introduced for online
coherency analysis. KHMC is insensitive to initialization of group centers and is fast. Besides, a
mechanism is developed to automatically determine the optimal number of groups during the online
analysis for KHMC. In this study, two types of clustering algorithms (hierarchical clustering and KHMC)
are elaborated based on IEEE 68-bus system.
5.2 Coherency analysis using hierarchical clustering
Hierarchical clustering is an algorithm that starts by regarding each of the generator as a separate
group. Thereafter, group merging is implemented to reduce the group numbers, and a dendrogram is
formed. In each iteration, two groups combine to form a new group. The y axis of the dendrogram is an
α-value, which is an index that measures the tightness of the clustering results, as defined in (5.1).
Generally, larger value of WSSE corresponds to smaller group number.[30]
2( )
2
( )
( )
i i j ii
i i alli
w x c
w x c
(5.1)
where cj(i) is the corresponding group center of a member xi, while call is the center of all the members in
all group. Thus the α-value can vary between zero and one.
The following steps are used during hierarchical clustering.
ii. Start by classifying each generator as a separate group.
iii. Identify two groups that are closest to each other.
iv. Merge the two closest groups. The new α-value can be updated incrementally.
v. Repeat ii and iii until all the generators are included in one group; and draw the dendrogram.
In the offline clustering, the generator speed deviation data are collected prior to the implementation
of clustering algorithm. In this study, a MATLAB program has been devised to visualize the dendrogram
42
for generator coherency using hierarchical clustering, which is a reflection of the overall closeness of
generators during transient performances.
The IEEE 68-bus 16-machine power system illustrated in Figure 5.1 is used in this study and is
simulated using the real-time digital simulator (RTDS). The following three cases indicates the impact of
operating condition on generator clustering.
Figure 5.1 IEEE 68-bus 16-machine power system. Coherent groups obtained using offline clustering is shown as colored regions
Case A: Fault happens at Generator 4 (at Bus 56) under normal load condition
The nearest load connected to Bus 56 is the load on Bus 20 of 680MW. The dendrogram and online
clustering result is shown in Fig 5.2. Since G4 and G5 are near the fault location, they oscillate in different
groups with each other as well as with other generators.
43
Figure 5.2 Dendrogram of generator coherency for Case A
Case B: Fault happens at connection line between Bus 2 and Bus 3 under normal load condition. In this
case, it is noticed that the generators in NE is oscillating coherently against those in NY, as shown in
Figure 5.3.
Figure 5.3 Dendrogram of generator coherency for Case B
44
Case 3 (The general case) PRBS signals are injected in the AVRs of all generators. Generator speed
deviations are measured. Accordingly, the clustering results of the dendrogram is shown in Figure 5.4.
Based on this case, an alpha-cut is applied to cluster the 16 generators in the IEEE 68-Bus power system
into five groups as documented in Table 5.1.
Table 5.1 Coherent generator groups for the general case
Group Generators Group 1 Group 2 Group 3 Group 4 Group 5
G1, G8 G2, G3 G4, G5, G6, G7, G9 G10, G11, G12, G,13 G14, G15, G,16
Figure 5.4 Dendrogram of generator coherency for Case C
0.7
0.75
0.8
0.85
0.9
0.95
1 8 4 7 5 6 9 10 11 12 13 2 3 14 15 161 8 4 7 5 6 9 10 11 12 13 2 3 14 15 161 8 4 7 5 6 9 10 11 12 13 2 3 14 15 16
Jaccard
dis
tance b
etw
een g
enera
tor
speed w
avefo
rms
alpha - cut
Generator Index
45
5.3 Coherency analysis using K-harmonic means clustering
In this section, a K-harmonic means clustering (KHMC) approach is applied for online coherency
analysis of synchronous generator. KHMC is a global optimizing algorithm that bases the adaptation of
the group centers based on the entire groups/clusters that exist prior. Unlike ordinary k-means clustering,
KHMC is insensitive to initialization of group centers and thus provides more accurate results [32-33].
Besides, the updated group center of a current time step can also serve as the initialization for the next
one; in this way, clustering results can be obtained at each consecutive time step, making KHMC very
suitable for online clustering. In order to decide the number of clusters in KHMC, an Average Within-
Group Distance (AWGD) threshold is adopted; groups may be merged or split to satisfy this threshold,
group number is thus decided indirectly.
5.3.1 Mathematical formulation
Common signals, x, used for coherency grouping are speed and speed deviations responses over a
window of time of generators. The distance between a generator i and a group center mk can be defined
as:
22
( ( ) ( ))ik i k i kj
d x m x j m j (5.2)
where j refers to the element index in a vector (xi or mk). Suppose there are K groups in total for all
the generators, the harmonic mean distance of generator i w.r.t to all group centers is defined as:
2
11/ (1/ )
ik
K
ik
D d
(5.3)
46
The determination of the optimal group centers is needed to properly classify coherent generators
together. The cost function to carry this out is defined as the weighed sum of iD for all generators, as
indicated below:
2minii
iJ H D (5.4)
where iH is the inertia constant of generator i. Generators with large H will dominate the cost function.
In order to minimize (5.4), the condition in (5.5) needs to be satisfied and if so, the group centers are
updated to minimize the cost function using (5.6).
4
31
2 ( ) 0ik
Ni i i k
ik
H D x mJm d
(5.5)
4 4
3 31 1
/ik ik
N Nnew i i i i ik
i i
H D x H Dmd d
(5.6)
where N is the number of generators in a power system. The centers are updated for every window until
the metric in (5.7) is satisfied or a maximum number of iterations is met. The KHMC based coherency
grouping is illustrated in Table 5.2.
20.01new
k km m (5.7)
Table 5.2 The Process of KHMC in Finding Group Centers
Step 1 Receive all the generator data (H, xi ) and initialize group centers mk;
Step 2 Calculate the distance dik between each generator i and group centers, mk, using (5.2);
Step 3 Update group centers using (5.6);
Step 4 If group centers becomes stable, then go to Step 5, otherwise, go back to Step 2
Step 5 Record the group centers, and stop.
47
The difference of KHMC from k-means clustering is its global convergence. In k-means clustering,
each group center only moves toward its closest generator at every step; this is a local adaption. In contrast,
for KHMC, change of every group center is dependent on all generators; each generator also affects all
group centers. Ultimately, the overall distance between each generator and its corresponding group center
is minimized as explained above. Besides, the adaption rule of (5.5)~(5.6) is much faster than gradient
descent; it also avoids the issue of deciding a learning ratio. This adaption rule is only realizable for
KHMC, not for k-means clustering. The robustness of KHMC makes it suitable for online clustering.
5.3.2 Online coherency grouping techniques
Online coherency grouping requires a stream of data of some window size. A power system model
is sampled to provide speed deviation signals of the generators at 10Hz. Clustering is made based on
generator speed deviation data of 2 seconds, i.e. a window size of 20 data points. For online analysis, a
moving window at 10Hz is used in this study. The KHMC algorithm is implemented in this study on a
remote processor from the one that simulates the power system. The clustering data is acquired through a
data acquisition system. The coherent groups are displayed on a screen.
Whenever a new window (has a new data point added at the end of the vector array, x and the first
data point of the previous window dropped) is received, group centers are updated using (5.2) ~ (5.7).
Since the window shifts by only one data point at each step, the group centers are located close to the old
ones, thus few iterations will be needed. The KHMC algorithm converges fast.
Once the group centers are determined each generator is assigned to its nearest group center
according to (5.8):
arg mini k ikk d (5.8)
48
Then decision-making whether to merge or split groups is made on a threshold. When a suitable
group number is achieved, the results are saved and dispatched for display to the user. The process repeats
for every window of data and is a continuous one.
5.3.3 Number of groups
It is generally assumed that group number K is predefined in KHMC; however, the value of K should
be updated for online generator coherency analysis.
A several methods for deciding of number of groups such as Alkaike information criteria approach
[34] and Silhoutte approach [35] exist. These methods make the decision on an index r = f(K) maximum
or minimum value reached when the value of K is optimal (where f(.) is a single-summit function).
However, for generator coherency grouping, a clear boundary of coherent areas may be vague in some
cases, and such index may not exist.
A better way is to set a threshold *1d for the average within -group distance 1d defined as:
1 , ( )1
i k ii
d dN
(5.9)
where ( )k i refers to the correspondent group index of generator i.
AWGD shows the cluster tightness; less AWGD corresponds to more groups. AWGD is a better
discriminant than Maximum Within-Group Distance (MWGD) [36]. K is decided as follows:
*1 1max{ | }K K d d ; (5.10)
In this study, the threshold of AWGD is defined as follows:
2*1 2
1
10.5N
ii
d xN
(5.11)
where xi is the speed deviation data set of generator i.
Based on (5.10), groups are merged or split according to two cases.
49
5.3.3.1 Group splitting
Number of groups should be increased by splitting an existing group that satisfies the condition in
(5.12a). This is achieved by splitting the group that has largest MWGD. Suppose generator i has the largest
distance towards its group center, during splitting, generator i is taken as a new group center as shown in
(5.11b). All other group centers are preserved.
*1 1d d (5.12a)
new ic x (5.12b)
5.3.3.2 Group merging
It is necessary to decide whether there are more groups than required. Two nearest groups should be
tentatively merged to check (5.13a) still holds. If it does, these two groups should be merges; otherwise,
the present group number is correct.
For merging these two groups i and j, whose inter-group distance is the smallest (with ci and cj are
their group centers, respectively), the new group center is computed using (5.13b).
Table 5.3 Group Merging and Splitting
Case Action
d1 > d1* Continue splitting groups by calling (5.12) and updating group centers through (5.1) ~ (5.6) until d1 < d1*.
d1 < d1* Continue merging groups by calling (5.13) and updating group centers through (5.1) ~ (5.6).
With the merger, the old groups i and j are deleted. This newly obtained group center needs to be
updated using (5.1) to (5.6) again. A summary of the process to determine the suitable number of groups
is illustrated in Table 5.3.
*1 1d d (5.13a)
50
i total i j total jnew
i total j total
H c H cc
H H
; (5.13b)
5.3.4 Offline and online clustering result
5.3.4.1 Offline clustering result
In Figure 5.5 the speed responses of 16 generators after a 50ms three-phase fault at the middle of
transmission line between buses 1 and 2 is shown. The blue lines corresponds to G1 and G8, green lines
corresponds to G2 and G3, yellow lines corresponds to G4, G5, G6, G7, G9, black lines corresponds to
G10, G10, G12, G13, and red lines corresponds to G14, G15, G16, G17. Table 5.3 shows the clustering
results for three cases studies. These cases investigate the effect of initialization of group centers for the
k-means and the KHMC.
Case 1: Using k-means clustering with poor initialization of group centers. All the initial centers are
zeros.
Case 2: Using k-means clustering with good initialization of group centers. Average of all generators
is taken for initial group centers.
Case 3: Using KHMC with poor initialization of group centers.
By visual inspection of Table 5.4 and Figure 5.5, it can be seen that Cases 2 and 3 yield better
clustering results than Case 1. k-means clustering works well only with proper group center initialization
values. However KHMC is insensitive to group center initialization values.
51
Figure 5.5 Speed responses of the sixteen generators in IEEE 68-Bus system
Table 5.4 Offline Clustering Result
Group Case 1 Case 2 Case 3
1 G1,G2,G8 G1,G8 G1,G8
2 G3 G2,G3 G2,G3
3 G4,G5,G6,G7,G9,
G10,G11
G4,G5,G6,G7,G9 G4,G5,G6,G7,G9
4 G12,G13 G10,G11,G12,G13 G10,G11,G12,G13
5 G14,G15,G16 G14,G15,G16 G14,G15,G16
5.3.4.2 Online clustering result
In online clustering, there might be different clustering result for each window of data. Generators
that are in the same group might be clustered into different group with the next window of data; however,
most coherent generators still tend to oscillate coherently.
Case I. 100ms three phase short circuit fault at bus 1.
A 100ms three-phase fault occurs at bus 1 at t = 3s. Shown in Figures 5.6 and 5.7 are the speed
responses of all 16 generators and online coherent generator groups, respectively. Table 5.5 presents
offline (using 18 seconds of speed data) and online (snapshots at three instances: 8s, 10s and 15s) coherent
0 2 4 6 8 10 12 14 16 180.99
0.995
1
1.005
1.01
Time [s]
speed in p
.u
52
generator groups using KHMC. Note that in the online clustering G1 and G8 are clustered in different
groups since they are close to the faulted bus.
Figure 5.6 Speed response of generators following fault at bus 1
Figure 5.7 Online coherent generator groups for a three phase short circuit fault at bus 1 in Figure 5.1
0 2 4 6 8 10 12 14 16 180.994
0.996
0.998
1
1.002
1.004
1.006
Time [s]
speed in p
.u.
0
5
10
15
20
0
5
10
15
201
2
3
4
5
6
7
Time [s]Generator index
Gro
up index
53
Table 5.5 Coherency Grouping Result for Case I
Group Offline Clustering
during 0~18s
Online Clustering
at 8s
Online Clustering
at 10s
Online Clustering
at 15s
1 G1 G1 G1 G1
2 G2,G3 G2,G3 G2,G3 G2,G3
3 G4,G5,G6,G7,G9 G4,G5,G6,G7,G9
G4,G5,G6,G7,G9 G4,G5,G6,G7,G9
4 G8 G8 G8 G8
5 G10,G11 G10 G10 G10,G11
6 G12,G13 G12,G13 G11,G12,G13 G12,G13
7 G14,G15,G16 G11,G14,G15,G16
G14,G15,G16 G14,G15,G16
Case II. 100ms three phase fault at bus 8.
A 100ms three-phase fault occurs at bus 8 at t = 3.5s. . Shown in Figures 5.8 and 5.9 are the speed
responses of all 16 generators and online coherent generator groups, respectively. At steady state before
the event happens, there is no oscillation, so that all 16 generators are clustered into one group. Later on,
clustering result might change in respect to time, but coherent generators still tend to be classified in same
groups.
Table 5.6 presents offline (using 18 seconds of speed data) and online (snapshots at three instances:
8s, 10s and 15s) coherency groups using KHMC. At 8s, G9 lost coherency with {G4, G5, G6, G7} for a
short while. G9 is much farther from the faulted bus than {G4, G5, G6, G7}. At 10s, adjacent groups {G1,
G8}, {G2, G3} and {G10, G11, G12, G13} merge.
54
Figure 5.8 Speed response of generators following fault at bus 8
Figure 5.9 Online coherent generator groups for a three phase short circuit fault
at bus 8 in Figure 5.1
0 2 4 6 8 10 12 14 16 180.994
0.996
0.998
1
1.002
1.004
1.006
Time [s]
speed in p
.u.
05
1015
20
0
5
10
15
201
2
3
4
5
6
7
8
Time [s]Generator index
Gro
up index
55
Table 5.6 Coherency Grouping Result for Case II
Group
index
Offline
Clustering during
0~18s
Online
Clustering at 8s
Online
Clustering at 10s
Online
Clustering at 15s
1 G1 G1,G8 G1,G2,G3, G8,G10,G11,G12,G13
G1,G8
2 G2,G3 G2,G3 G4,G5,G6,G7,G9 G2,G3
3 G4,G5,G6,
G7,G9
G4,G5,G6,G7 G14,G15,G16 G4,G5,G6,
G7,G9
4 G8 G9 G10,G11, G12,G13
5 G10,G11 G10,G11 G14,G15, G16
6 G12,G13 G12,G13
7 G14,G15,G16 G14,G15,G16
5.4 Summary
This chapter elaborated the methodology of generator clustering under different operating conditions
using two approaches: hierarchical clustering and KHMC. The former is suitable for drawing a detailed
dendrogram during offline clustering, while the latter is suitable for both offline and online clustering. The
offline clustering results yielded by these two approaches agree with each other under the basic operation
condition. With the KHMC based clustering algorithm, change of generator coherency during power
system transient can be captured.
56
CHAPTER 6
COHERENCY BASED DAMPING CONTROLLER
6.1 Introduction
There are many methods for damping oscillations in a power system. Traditional PSSs are installed
to damp local and intra-area oscillations, as elaborated in Chapter 4. Generally, the PSSs use respective
generator speed deviation signals as input signals to generate supplementary control signals that are
provided to Automatic Voltage Regulators (AVRs). However, locally measured generator speed signal
may not contain sufficient information to uncover the characteristics of inter-area oscillation modes [5];
as a result, local PSSs are not effective to damp inter-area oscillations. Fortunately, with the deployment
of Phasor Measurement Units (PMUs) in the power system, speed signals from remote generators can be
made available as additional input signals for the design of advanced damping controllers.
As for damping controller design using remote measurements, an overview of a Wide Area Control
(WAC) system structure is suggested in [6]; the importance of WAC using PMU data to maintain power
system stability is elaborated. Though a fuzzy controller making use of PMU measurements of voltages
and reactive powers is able to maintain voltage stability, the control approach by capacitor/reactor bank
switching may not be swift and accurate enough to damp inter-area oscillations. A two-area system based
real-time implementation of a wide-area controller by AVR supplementary control considering
communication delays is presented in [37]. The design approach in [37] is completely data-driven, with
the control law implemented by a neural network providing supplementary control signals to all generators.
For large power systems, it may not be practical to provide supplementary control to all generators. In
[38], WAC is applied to a large power system based on a linearized mathematical model; effective
57
measurement and control signals to damp inter-area oscillations are selected using geometric approach.
However, the damping control signal is based on a single remote measurement; and an accurate model of
a large power system is difficult to obtain. An innovative damping control method is implemented without
designing any wide area controllers in [39]. The local PSSs’ outputs are combined a matrix gain to
generate modulated PSS signals to the AVRs in a 12 bus power system with three generators. The optimal
matrix for modulating the initial PSS signals was obtained using the particle swarm optimization algorithm.
However, this approach is not directly applicable for larger power systems due to increased matrix size;
besides, since the local controllers have been designed only to address the local and intra-area oscillations,
they may not work effectively at the frequency range of inter-area oscillations. A typical H∞ wide-area
PSS design is proposed in [40]. Despite of the robustness of designed controller to uncertain system
parameters, the design with pole-placement constraints may not have a solution; also, since general H∞
design achieves a controller with the same order with system states; it has to be further reduced to form a
PSS at the risk of reduced efficacy. In [1], the concept of Virtual Generator (VG) is applied in design of a
single-input multiple-output controller using adaptive critic designs; it is indicated that a VG is a
mathematical equivalent of a group of generators that tend to oscillate coherently in response to
disturbances. However, the damping controller uses only one VG speed; this may not provide sufficient
information to damp inter-area oscillations over a wide range of operating conditions.
In this study, power system conditions that give rise to inter-area oscillations using Stochastic
Subspace Identification (SSI) based modal analysis are studied; and a new approach to implement
supplementary PSS based on VGs (VG-PSS) to damp inter-area oscillations is presented, as shown in
Figure 6.1. Speed deviations from all the large generation units are remotely measured and sent to a control
center, which implements coherency analysis and uses the proposed VG-PSS to generate a supplementary
control signal. The generator choice for the supplementary control location is determined based on the
58
generator that has maximum controllability on dominant weakly damped inter-area mode(s) in a power
system. The overall flowchart of the suggested design approach is shown in Figure 6.2, which is further
elaborated in theoretical details in following sections.
Figure 6.1 The diagram of the proposed control scheme with VG-PSS
𝐺1 𝐺2 𝐺3 𝐺𝑅
Time delay
𝜏1 𝜏2 𝜏3 𝜏𝑁 𝜏R
Control Center
Coherency Analysis
PSS + Time-delay compensator
VG - PSS
𝑉′𝑉𝐺−𝑃𝑆𝑆
𝜔1 𝜔2 𝜔3 𝜔𝑟 𝜔N
𝜔𝑉𝐺2 𝜔𝑉𝐺−𝑀
Supplementary control signalPower System
Generators 𝐺𝑁
𝜏control
…
… …
Synchronization
𝜔′1 𝜔′2 𝜔′3 𝜔′𝑟 𝜔′N
(𝑡)
(𝑡) (𝑡) (𝑡) (𝑡) (𝑡)
𝜔VG1 (𝑡) (𝑡) (𝑡)
(𝑡) (𝑡) (𝑡) (𝑡) (𝑡)
𝑉𝑉𝐺−𝑃𝑆𝑆 (𝑡)
59
Figure 6.2 The overall flowchart of design approach
6.2 Development of VG-PSS
In this section, a VG-PSS that is heuristically tuned according to modal analysis results, is proposed
for supplementary damping control. The modal analysis presented is based on a data-driven system
identification approach. In addition, the determination of virtual generator(s) based on coherency analysis
is presented and the tuning of VG-PSS is elaborated in the following sub-sections.
6.2.1 Modal analysis based on system matrices
Besides facilitating controller design, modal analysis also provides a way to exam the efficacy of a
controller. Prior to performing modal analysis, it is necessary to obtain a model for the power system
without detailed mathematical model of every component that captures the full dynamics. Chapter 3 has
elaborated an approach to obtain system matrices and to carry out modal analysis. In this study, the AVRs
Start
SSI-based system identification
Modal analysis
Power system simulation under contingency
Cost function calculation
Update of VG-PSS parameters using PSO
Maximum iteration achieved ?
Y
N
End
Verification of results
60
of all the generators are regarded as the system inputs where PRBSs are injected as disturbances to trigger
power system transients, while the speed deviations of all the generators are measured as outputs. With
the application of SSI algorithm, the system matrices A,B,C,D are identified. Thereafter, the observability
and controllability factors for each generators can be calculated. It can be seen from Figure 3.5 that the
generator G8 and G9 are with the highest controllability factor; thus, damping controller output can be
applied on G8 and G9.
6.2.2 Inter-area oscillation analysis
Inter-area oscillation refers to the phenomenon where two areas in a power system oscillate against
each other generally at a low frequency. These areas may contain one or more synchronous generators.
When the operating condition is pushed toward stability limit in a power system, oscillations may occur
due to lack of damping torque as can be identified using techniques elaborated in Chapter 3. The modes
of oscillations are largely determined by the power system topology, as well as the parameters of
generators and transmission lines. In Chapter 2, it has been verified that as the active power transfer from
NE to NY increases, the power flow in the transmission lines rises, and the damping torque for the 0.22
Hz oscillation between NE and NY decreases. The operating condition with high active power transfer
from NE to NY serves as benchmark to verify the effectiveness of damping controller designed in this
study.
6.2.3 Structure of VG-PSS
The traditional structures of local PSSs are composed of a washout component, a lead-lag
compensator and a magnitude limiter. Through compensation of phase angle at a specific oscillation mode,
a torque is made exactly in opposite phase of speed deviation, leading to increased damping ratio.
However, according to the analysis, local PSSs may not effectively deal with inter-area oscillation modes,
for the generators of maximum controllability are not necessarily with maximum observability. In
61
contrast, a PSS using remote measurement is more capable to provide damping torque for inter-area
oscillations. In previous research of Wide Area Control (WAC), the input signal to the controller uses
either the speed deviation of one generator of maximum observability or the difference of average speed
between two the groups of generators that are oscillating against each other. In this research, on basis of
the local PSS structure, a proposed VG- PSS is shown in Figure 6.3.
Figure 6.3 The proposed structure of VG-PSS
Taken as the inputs are the virtual generator speeds that are mathematical simplification for groups
of coherent generators, as explained in detail in the coming sections. AVR supplementary signal at
generator of maximum controllability is taken as the output. This PSS is expected to make use of wide
area information to stabilize the power system. Ten parameters are to be decided. The value of K1~KM
reflect the impact of each virtual generator speed on the control efficacy; larger values of Ki signifies that
the ith virtual generator has larger engagement in this oscillation. T1~T4 reflect the oscillation frequency
as well as the compensation angle. Although the concerned frequency range of the proposed PSS differs
from that of local PSSs, its parameters will be configured in an intelligent way as in the analysis of
following sections.
In this approach, a heuristic algorithm Particle Swarm Optimization (PSO) is deployed to tune the
parameters. The optimal parameters will be reached by repetitively testing the efficacy of each set of
𝐾1
𝐾2
𝐾3
……
……
𝐾𝑀
Σ 10𝑠
1 + 10𝑠𝐾0
𝑇1𝑠 + 1
𝑇2𝑠 + 1
𝑇3𝑠 + 1
𝑇4𝑠 + 1𝐾𝐶
1 + 𝑠𝑇𝐶11 + 𝑠𝑇𝐶2
2
Δ 𝜔𝑉𝐺1
Δ 𝜔𝑉𝐺2
Δ 𝜔𝑉𝐺3
Δ 𝜔𝑉𝐺−𝑀
𝑉𝑜
0.1
−0.1 Washout Time-delay compensator Limiter
62
WAPSS parameters using 20 particles. During the tuning process, the cost function for each set of
parameters is figured out through real-time simulation on Real-Time Digital Simulator (RTDS) with the
full model of every component in the power system.
6.2.4 Determination of virtual generators
Though damping control is applied using remotely measured signals, the large scale of power system
makes it prohibitive to take all generator speed responses as the controller input. Fortunately, it has been
shown in Chapter 4 that generators generally oscillate in coherent groups. Generally, generators with small
electrical distance show similarity in speed responses following a contingency. A Virtual Generator (VG)
is a mathematical equivalent of a group of coherent generators. A complicated multi-machine power
system can be significantly simplified with the concept of virtual generators. To achieve this, hierarchical
clustering algorithm can be applied based on the speed response data of all generators; a dendrogram is
yielded so that the generators are classified into several groups under certain threshold.
In this approach, four steps are introduced to obtain the virtual generators in a power system,
i. The power system is disturbed with PRBS injection [41] at the supplementary input site of
each generator; and speed responses of all generators are collected.
ii. A hierarchical clustering algorithm is implemented and the diagram is formed showing the
coherency of generators.
iii. Through visual inspection, an α-cut threshold is decided and the groupings of generators
are formed [23].
iv. The virtual generator speed for each group can be calculated using the formula,
1 1 2 2
1 2
......
n n
i
n
i i i i i iVG
i i i
H H HH H H
(6.1)
It can be seen from (6.1) that two conditions must be satisfied in order to calculate the VG speeds:
first, all the local generator speeds need to be observable by a control center (Figure 6.1) that executes the
63
calculation. With the advent of Phasor Measurement Units (PMUs), the real-time variation of frequency
at each generator bus can be measured, which is directly linked with the generator speed deviations. For
a larger system that covers large geographic domain with large number of generators, PMUs are installed
on a limited selection of generators that best represents system dynamics and helps deriving the virtual
generator model in each coherent group. Second, the measured frequencies from all generator buses are
real-time data flows and thus need to be synchronized. Fortunately, PMU is able to give each measured
data with a time stamp with the aid of a Global Positioning System (GPS) radio clock, as a result, the
synchronization of real-time measurement at all the generators can be realized. A time-delay is resulted
during the synchronization and communication of remote PMU data to the control center.
It is computationally and practically challenging to design a supplementary controller making use of
all generator speeds especially for a large power system nor is it necessary. A VG is a good representation
of a group of generators that behave in a similar manner. Although the concept of VG is originally
suggested as mathematical simplification of multiple generators, the determination of VGs is data-based.
The clustering/grouping approach uses the measured speed responses of generators following PRBS
disturbances at the AVRs of all generators, which represents the coherency of generators in a general
sense, and is a better approach rather than a clustering approach following a fault or an increase of
generation, as has been observed in [11] that the site and type of fault can largely impact the coherency of
generators. Considering that the generator coherency is subjected to change of operating conditions and
contingencies, variation in generator coherency occurs. However, based on the fact that geologically
adjacent generators tend to oscillate coherently, and that contingencies only lead to very slight change of
the overall power system topology, the proposed virtual generator modelling based on fixed coherent
groups is assumed in this study. Though efficacy of this design is demonstrated in the simulation results,
64
future research will use artificial immune system based adaptive controller to handle the variation of
generator coherency, leading to improved damping effectiveness.
6.2.5 PSO for VG-PSS tuning
Particle Swarm Optimization (PSO) is an adaptive algorithm that heuristically searches best
solutions with swarm intelligence; it is widely used for parameter tuning [42]. The parameters to be
determined are mirrored to the positions of particles; and a fitness function to be minimized is defined as
a satisfactoriness measurement for a set of parameters. To search for a minimal value of fitness function,
each particle keeps updating its position by actively moving toward the local and global optimum point,
respectively defined as the historical position of its own and of all particles that correspond to the smallest
fitness function value. During the optimization, the fitness function is monotonically decreasing until all
particles coherently converge to a global optimal position in a final stage. Due to its robustness to nonlinear
non-convex problems, PSO is adopted in this study to optimize the parameters of VG-PSS. The following
part of this section elaborates technical details for implementation, including the determination of fitness
function and the algorithm of parameter updating.
In this study, the position of a particle pi represents the set of all parameters corresponding to Figure
6.3, thus ,1 ,2 , ,1 ,2 ,3 ,4[ , ,..., , , , , ]i i i i M i i i ip K K K T T T T . Under this set of parameters, speed responses following a fault
are obtained through simulation; and a fitness function is required to analyse the speed responses. There
are generally two ways to determine the fitness function: through either frequency domain or time domain.
Since it is expected that a decreased oscillation be observed from the speed responses with the effect of
controller, the damping ratio under the concerned frequency can be taken as the cost function, which is
obtained by modal analysis of speed deviation simulation results. Experiments using this frequency-
domain based cost function shows ability to reject unexpected oscillation modes brought by the new set
of parameters obtained in the optimizing process. Alternatively, a cost function can be straightforwardly
65
defined by analysing the time series of speed response curves; for example, the H2-norm (i.e. squared
mean average through time) of speed responses can be taking as the cost function. Time-domain based
cost function leads to a better final-stage performance despite of slow convergence. It is desired to
combine the merits of both these two options: a frequency-domain part of the cost function is expected to
play a more important role at the first stage so that the particles approaches an appropriate solution with a
fast speed, while a time-domain part of cost function improves the efficacy of controller at the final stage.
Thus, the following cost function is adopted:
20
1 1min{ , } ( ( ))
GN N
f ii j
J j
(6.2)
in which ξf denotes the damping ratio near the frequency f; ( )i j denotes the speed deviation the i’th
generator at the time step j; α is a large real value; and ξ0 denotes a threshold of damping ratio; NG is the
generator number, while N is the length of data points. At the beginning of tuning process, since the
damping ratio under parameters of most particles may be very low, the judgement of performance is
mainly decided first term in (6.2). However, as the performance of each particle improves so that the
damping ratio ξf is larger than the threshold ξ0, the performance is only dependent on the second term that
reflects the speed deviation profiles of all generators. The parameters are further adjusted to minimize the
second term so that performance is further improved.
Define pi,lbest and pgbest as the local and global optimum point of particle pi respectively. At each
iteration, all particles are updated through (6.3) ~ (6.4). For all i’s.
, 0 , 1 1 , , 1 2 , 1( ) ( )i k i k i lbest i k gbest i kv v p p p p (6.3)
, 1 , ,i k i k i kp p v (6.4)
Meanwhile, whenever the cost fitness function is calculated with the updated particle position, ,i lbestp
and gbestp are also updated through (6.5) and (6.6).
66
, ,min{ , }new oldi lbest i lbest ip p p ; (6.5)
min{ , }new oldg g ip p p ; (6.6)
In the final stage, all the particles ultimately converge to a solution, and is taken as the solutions.
Shown in Figure 6.4 is flowchart of PSO parameter-tuning algorithm based on the speed deviation data
following PRBS injection at all the AVRs.
Figure 6.4 PSO flowchart for VG-PSS parameters tuning algorithm.
Update of local and global optimum using (6.5)~(6.6)
Start
Initialization of VG-PSS parameters
Go to the next particle, determination of fitness function using (6.2)
Iterations >= Reference?
Update of Parameters using (6.3) ~ (6.4)
Y
N
End
All particles iterated?
Y
N
67
6.2.6 PSO versus other design techniques
Numerous techniques exist for the design of supplementary damping controllers. Traditional pole-
placement is effectively applied for design of single-input single-output controller [29], yet it is not the
only way; other approaches such as bacterial foraging algorithm (BFA) and adaptive critic designs (ACDs)
have also been used for wide area controller designs, as shown in [43] and [44]. For this study, since the
proposed VG-PSS uses speed deviations of multiple VGs, and the contribution of each VG for the control
signal is unknown, it is preferred to use the PSO-based heuristic approach in this study. Also, despite its
robustness, H∞-based approach yields several high-order separate controllers linking each VG speed
deviation input to the controller output; in contrast, there are limited amount of parameters in the proposed
VG-PSS that can be realized with a traditional lead-lag structure. With a simple mathematical form, the
VG-PSS establishes a standard schematic for the supplementary damping control, with the parameters
best tuned by PSO. The effectiveness of VG-PSS controller is presented in Section 6.3.
6.2.7 Time delay compensation
In the proposed VG-PSS, time delay is incurred about in two processes: (i) τPMU: the communication
between the control center and the PMUs; (ii) τcontrol: the communication between the control center and
the generator that the supplementary control is applied too. In this study, these two time delays are merged
as τ = τPMU + τcontrol, and is compensator inside the VG-PSS by the transfer function given in (6.7).
2
1
2
1( )1
CC C
C
T sG s KT s
(6.7)
where 11 1 sin( / 2)
1 sin( / 2)CT
and 2
1 1 sin( / 2)1 sin( / 2)CT
. ω is the oscillation frequency of concern. KC is
normalized so that ( ) 1CG j . This compensator is able to effectively provide a phase angle
compensation at the oscillation frequency of concern ω [45]. For a wide area control system, time delay
68
τ can be determined with the aid of GPS clock labels included in the PMU data. In this study, τ is assumed
to be time-invariant.
6.3 Simulation results
The contingency used for PSO tuning is a 50ms fault on Bus 27. Corresponding to different
contingencies, three case studies are shown to indicate the efficacy of VG-PSS damping controller. For
each of them, the VG-PSS is installed either on G8 or on G9. With VG-PSS on G8 or G9; and the
optimized parameters are shown in Table 6.1. In case studies I to III, a time delay of 100ms is considered.
Table 6.1 The optimized parameters of the VG-PSS
Parameters Case I
With VG-PSS on G8
Case II
With VG-PSS on G9
1K 0.9587 -0.2318
2K 0.363 -0.0524
3K -1.00 0.8703
4K -0.7126 0.5533
5K 1.00 0.9963
0K 25 19.2026
1T 1.5416 0.4680
2T 0.4024 0.7744
3T 5.2393 6.8278
4T 4.1175 2.7501
Case Study I: The system is originally at operating condition II presented in the appendix Table A.1.
A 50ms three-phase fault takes place at Bus 2, causing the tripping of transmission lines between Bus 1
and Bus 2. Shown in Figure 6.5 are the speed deviation responses of selected generators, the VG-PSS is
installed on G9.
69
Figure 6.5 Case Study I -- The speed deviations plots of selected generators with VG-PSS on G9.
Through modal analysis, with no PSSs, the damping ratio is 0.4%, and the power system is
marginally stable; with only the local PSSs, the damping ratio is 6.1%, while with only the VG-PSS
installation on G9, the damping ratio is 11.6%, with the cooperation of VG-PSS with local PSSs, the
damping ratio improved to 28.9%.
The VG-PSS installed on G8 shows similar effectiveness as shown in Figure 6.6. In order to verify
that the two VG-PSSs can be working cooperatively, Figure 6.6 compares the control effect with both
0 5 10 15 20 25-4
-2
0
2
4
x 10-3 G1
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-4
-2
0
2
4x 10
-3 G4
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-4
-2
0
2
4
x 10-3 G8
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-4
-2
0
2
4x 10
-3 G9
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-1
0
1x 10
-3 G13
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G14
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G15
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G16
Time : s
Speed d
ev :
p.u
.
No PSSs
With local PSSs
With VG-PSS
Local PSSs & VG-PSS
70
VG-PSSs and with only one VG-PSS installed on G8 or G9. It can be concluded that, when VG-PSSs are
installed on both G8 and G9, better damping effectiveness is achieved than VG-PSS installed on each
individual generator. Even without installation of local PSSs, the cooperating VG-PSSs are able to provide
significant damping torque.
Figure 6.6 Case Study I -- The speed deviations plots of selected generators for different sites of
VG-PSS installations.
0 5 10 15 20
-2
0
2
4
x 10-3 G1
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20
-2
0
2
4
x 10-3 G4
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-4
-2
0
2
4
x 10-3 G8
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20
-2
0
2
4
x 10-3 G9
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-1
0
1x 10
-3 G13
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G14
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G15
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G16
Time : s
Speed d
ev :
p.u
.
VG-PSS on G9
VG-PSS on G8
VG-PSS on G8 and G9
Local PSSs & VG-PSS on G8 and G9
71
Case Study II.A: With the transmission line Bus1–Bus2 already tripped, the system changes to
operating condition III.A in the appendix Table A.1. A 50ms three-phase fault happened at Bus 8. Shown
in Figure 6.7 are the speed deviation responses of selected generators.
Figure 6.7 Case Study II.A -- The speed deviations plots of selected generators with VG-PSS on
G9.
0 5 10 15 20 25
-2
0
2
x 10-3 G1
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25
-2
0
2
x 10-3 G4
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25
-2
0
2
x 10-3 G8
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25
-2
0
2
x 10-3 G9
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-1
0
1x 10
-3 G13
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G14
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G15
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G16
Time : s
Speed d
ev :
p.u
.
No PSSs
With local PSSs
With VG-PSS
Local PSSs & VG-PSS
72
Without local PSSs and VG-PSS, the power system becomes unstable following the contingency.
Through modal analysis, with only the local PSSs, the damping ratio is only 0.5% which is close to the
stability margin; with only the VG-PSS on G9, the damping ratio improves to 7.5%; and with both local
PSSs and the VG-PSS on G9, the damping ratio improves to 16.87%. Figure 6.8 compares the control
effect with both VG-PSSs and with only one VG-PSS installed on G8 or G9 showing the ability of
cooperating VG-PSSs to improve the damping effectiveness.
Figure 6.8 Case Study II.A -- The speed deviations plots of selected generators for different sites of VG-PSS installations.
VG-PSS on G9
VG-PSS on G8
VG-PSS on G8 and G9
Local PSSs & VG-PSS on G8 and G9
0 5 10 15 20
-2
0
2
4x 10
-3 G1
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20
-2
0
2
4x 10
-3 G4
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-4
-2
0
2
4x 10
-3 G8
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20
-2
0
2
4x 10
-3 G9
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-1
0
1x 10
-3 G13
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G14
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G15
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G16
Time : s
Speed d
ev :
p.u
.
73
Case Study II.B: The system changes to operating condition III.B listed in Table A.1 in the appendix.
Comparing to Case Study II.A, the load on Bus 1 has increased by 100%, from 256 MVA to 512 MVA.
The increased active power is supplied by G13. The same contingency as in Case Study II.A is applied
and the speed deviation responses of selected generators are shown in Figure 6.9.
Figure 6.9 Case Study II.B -- The speed deviations plots of selected generators with VG-PSS on G9 under a new load condition
Without local PSSs and VG-PSS, the power system becomes unstable following the contingency.
Through modal analysis, with only the local PSSs, the damping ratio is only 1.5% which is close to the
0 5 10 15 20
-2
0
2
x 10-3 G1
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-4
-2
0
2
4x 10
-3 G4
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20
-2
0
2
x 10-3 G8
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-4
-2
0
2
4x 10
-3 G9
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-1
0
1x 10
-3 G13
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G14
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G15
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G16
Time : s
Speed d
ev :
p.u
.
No PSSs
With local PSSs
With VG-PSS
Local PSSs & VG-PSS
74
stability margin; with only the VG-PSS on G9, the damping ratio improves to 7.9%; and with both local
PSSs and the VG-PSS on G9, the damping ratio improves to 17.54%.
Case Study III: The system operation is changed to operating condition IV as shown in Table A.1 in
the appendix. A 50ms three-phase fault is applied at Bus 27. Shown in Figure 6.9 are the speed deviation
responses of selected generators.
Figure 6.10 Case Study III -- The speed deviations plots of selected generators with VG-PSS on G9.
In this case, whether local PSSs are installed or not, if VG-PSS is not installed, the system becomes
unstable following the contingency. With the VG-PSS installed, damping ratio is 6.2% without local PSSs,
and is 11.2% when local PSSs are installed. Figure 6.10 compares the control effect with both VG-PSSs
0 5 10 15 20 25
-2
0
2
4x 10
-3 G1
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25
-2
0
2
x 10-3 G4
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25
-2
0
2
4x 10
-3 G8
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25
-2
0
2
4
x 10-3 G9
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-1
0
1x 10
-3 G13
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G14
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G15
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20 25-2
0
2x 10
-3 G16
Time : s
Speed d
ev :
p.u
.
With local PSSs
With VG-PSS
Local PSSs & VG-PSS
and with only one VG-PSS installed on G8 or G9, and same conclusions can be drawn as for Case Studies
I and II.
Figure 6.11 Case Study III -- The speed deviations plots of selected generators for different sites of VG-PSS installations.
It can be seen from Figures 5 ~ 10 that with the VG- PSS implementation, the power system settles
to steady state much faster. Also, the damping ratios are improved. Thus, the designed VG-PSS(s) is able
to stabilize the power system for all these three cases. The settling time of the generator speed deviations
(shown in Figures 6.5, 6.7, 6.9 and 6.10) for case studies I, II and III are given in Table 6.2. Herein, the
settling time is defined as the time it takes for the oscillations to settle within ±5% of the maximum speed
75
0 5 10 15 20
-2
0
2
4x 10
-3 G1
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20
-2
0
2
4x 10
-3 G4
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-4
-2
0
2
4x 10
-3 G8
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-4
-2
0
2
4
x 10-3 G9
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G13
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G14
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G15
Time : s
Speed d
ev :
p.u
.
0 5 10 15 20-2
0
2x 10
-3 G16
Time : s
Speed d
ev :
p.u
.
VG-PSS on G9
VG-PSS on G8
VG-PSS on G8 and G9
Local PSSs & VG-PSS on G8 and G9
76
deviation. Again, it can be observed that VG-PSSs in combination with local PSSs provides the minimal
settling time in all three case studies.
Table 6.2 Settling time of generator speed deviations for the three case studies (in seconds)
Cases With no PSSs
(s)
With only local PSSs
(s)
With only VG-PSSs on G8
(s)
With only VG-PSSs on G9
(s)
With both VG-PSSs
and local PSSs
(s)
Case Study I >50 28.2 14.6 16.4 6.1
Case Study II.A Unstable >50 26.6 27.6 7.2
Case Study II.B Unstable >50 24.6 26.5 7.0
Case Study III Unstable Unstable 36.2 40.8 8.8
The effectiveness of time-delay compensators is shown in Figure 6.12. The comparison of speed
responses with and without the time-delay compensators for G9 are plotted for different time delays under
Case Study II. It can be seen that without compensation, the control effect worsens as the time-delay
increases (Figure 6.12(c)). However, the proposed compensator is able to counteract the time delay and
improve the damping effectiveness.
77
Figure 6.12 Impact of time delay for the speed responses at G9.
(a) 50ms time delay (b) 100ms time delay (c)200ms time delay
6.4 Summary
In this study, SSI-based modal analysis is used first to identify the operating conditions that give rise
to inter-area oscillation. It is shown that oscillation occurs when the center of generation does not overlap
with the load center. The concept of virtual generators is used to cluster the synchronous generators into
several coherent groups in an offline manner. Based on the VGs determined, supplementary wide area
controller using virtual generator speeds is developed. The particle swarm optimization algorithm is
applied to determine the optimized parameters of VG-PSS. Real-time simulation of the IEEE 68-bus
system with VG-PSS(s) have illustrated the enhanced damping of the proposed approach for damping
inter-area oscillations and maintaining the stability of a power system.
0 5 10 15 20-2
0
2
x 10-3
Time : s
(a)
Spee
d de
viat
ion
: p.u
.
0 5 10 15 20-2
0
2
x 10-3
Time : s
(b)
Spee
d de
viat
ion
: p.u
.
0 5 10 15 20-2
0
2
x 10-3
Time : s
(c)
Spee
d de
viat
ion
: p.u
.
With only local PSSs
Local PSSs and VG-PSS
without compensation for time delay
Local PSSs and VG-PSS
with compensation for time delay
78
CHAPTER 7
ADAPTIVE DAMPING CONTROLLER
7.1 Introduction
Traditionally, remote measurements based damping controllers have fixed parameters. In [38], inter-
area oscillations are damped by static VAR compensator based on optimal measurement signal selection.
In [46], WAC is implemented through phase compensation. An earlier study that shows a virtual generator
based power system stabilizer (VG-PSS) for damping of inter-area oscillation modes is reported in [13].
This VG-PSS uses remotely measured virtual generator speeds for supplementary damping control at the
generator of maximum controllability. These above-mentioned controllers have fixed parameters.
However, it is desired that the parameters self-tune online so that the controllers are adaptive to various
changing conditions that affect control effectiveness and system performance.
In [47], a conventional multiple-model adaptive control scheme is applied to form a control signal
from a bank of controllers; yet the number of operating conditions corresponding to each pre-designed
controller is limited. A neural-network based adaptive critic control scheme for WAC is suggested in [1];
however, the update of neural networks parameters is offline, thus the parameters of this controller remain
unchanged during the real-time operation of the power system. In [48], artificial immune system (AIS) is
introduced for adaptive excitation control of generators in an electric ship to handle high energy demand
loads such as pulsed loads. The conception of AIS provides a good methodology for development of an
adaptive controller. Since the parameters of controllers can be automatically changed in response to
different states, the controllers are able to operate under more critical operating conditions.
79
7.2 Problem formulation
In this study, the concept of AIS is applied for the development of a wide area signals based adaptive
damping controller for inter-area oscillations. Based on an optimal (innate) controller with best tuned
parameters developed in [13], the AIS further modifies the control policy by temporarily adjusting
controller parameters for unseen and abnormal disturbances. This is the second aspect of the AIS concept:
an adaptive immune controller. The wide area signals are derived from virtual generators formed by
coherency grouping. Each coherent group is modeled by a virtual generator. Comparing to a damping
controller with fixed parameters, the AIS-based control is more agile and can stabilize a power system
under various operating conditions and disturbances due to its innate and adaptive immune properties. By
modeling biological immune systems, AIS adaptively and interactively generates feedback control signals
to restore a system to its steady state. During the development of the optimal controller, generators in the
power system are assumed to be oscillating in fixed coherent groups. However, it is known that a variation
of operating conditions could lead to different coherent groups. For instance, generators near the fault site
tend to lose oscillatory coherency [1]. Thus, the performance of the innate controller is degraded. Besides,
since the oscillations occur in multiple frequencies during transients, a control with fixed parameters may
not be robust enough to handle with the complicated power system dynamics. Fortunately, the impact of
new coherent groups and multiple modes can be minimized by adaptive nature of the AIS.
7.3 Artificial immune system
The defensiveness of a biological immune system relies on the presence of innate and adaptive
immunity. As an analogy to a biological immune system that is resistant to antigen incursion, AIS can
provide enhanced power system stability by improving controller adaptiveness to disturbances and
contingencies. To maximize control effectiveness, an AIS based adaptive controller is introduced in this
study. In the application of AIS, the innate immunity is realized through optimal parameter configuration,
80
and the adaptive immunity is realized through adaptive change of controller parameters, as elaborated in
the following subsections.
7.3.1 Innate immunity
In the biological immune system, innate immunity refers to the ability of living body (such as human)
to provide the primary defense reactions against incurring antigens by generating neutrophils (such as
blood cells) to identify and destroy the antigens. The antigens are bound and engulfed by macrophages
before being further demolished by neutrophils like white blood cells. The control mechanism in innate
immunity is the ability to generate a control signal to maintain stability in response to the measured
perturbation from equilibrium. This response behavior can be achieved by an optimal action and can be
compared to a control system with fixed parameters.
7.3.2 Adaptive immunity
In the biological immune system, the dendritic cells that bind antigens can be further evolved into
antigen presenting cells (APCs), B cells and T cells. Based on this, a more sophisticated feedback law
mechanism to provide adaptive immunity is present. When an antigen is detected in a living body, APC
is generated that leads to the production of helper T cells. The helper T cells further activate B cells and
killer T cells that swallow and annihilate the antigen. The suppressor T cells function to hinder the activity
of all other cells activated by helper T cells as illustrated in Figure 7.1 [12].
A feedback mechanism adaptively regulates the activity of cells. The presence of invading antigens
leads to more activated helper T cells that significantly increase the amount of killer T cells and B cells.
Over time when the antigens diminish and helper T cells decrease in activity, both killer T cells and B
cells are inhibited by suppressor T cells that have been already generated. Ultimately, the antigens are
completely diminished, and killer T cells and B cells are deactivated.
81
Figure 7.1 A biological immune system
In an AIS-based controlled system, as soon as the system moves away from its steady state, the
controller parameters are regulated over time to restore the system to its steady state as quickly as possible.
The deviation of the controlled system from its steady state is analogous to the antigen, while the amount
of T cells and B cells is analogous to the regulation of controller parameters. When steady state has been
achieved, the controller parameters return to their innate values.
The nominal value for each of the N controller parameters is denoted as pi,standard (i = 1,2, … N). The
deviation of parameter at the moment of k is denoted as Δpi(k) as indicated in (7.1). The mechanism of
parameter updating process using AIS is shown in Figure 7.2.
,standard( ) ( )i i ip k p p k (7.1)
where
( ) ( ) ( )i i ip k TH k TS k (7.2)
Antigen
APC
Helper T Cell
Suppressor T Cell
B Cell Killer T Cell
- - -
+
+
+ +
+
--
82
Figure 7.2 The schematic of the proposed AIS based control for a dynamic system.
It is comprised of two competing terms. The first term is analogous to helper T cells that activates
the control effect; and is directly proportional to Δz as expressed in (7.3), where mi1 is a stimulation factor
to the gain of helper T cells.
1( ) ( )i iTH k m z k (7.3)
The second term in (7.2) corresponds to suppressor T cells that diminish the control effect. It is
inversely related to the amplitude of the changing rate at Δz. TSi (k) can be expressed as (7.4), in which
mi2 is an inhibition factor related to the gain of suppressor T cells. According to (7.4), the faster declining
rate of Δz leads to the larger value of TSi(k), which counteracts the parameter change brought by THi (k).
The output of division block in Figure 7.2 is reset to zero when steady state is reached.
2
2( )( ) exp
( 1)i iz kTS k m z
z k
(7.4)
÷ ÷
×
×
Σ −
+
Optimal controller with parameters pi(k)
Controller output, Δy(k)
System output, Δz(k)
Change of parameters, Δpi(k)
mi1(k)
mi2(k)
THi(k)
TSi(k) exp(-x2) z-1
Δzi (k-1)
Controlled System
System reference input, X ref (k) Disturbance, d(k)
Δz(k)
83
Equations (7.1)-(7.4) can also be applied for the update of any other controller parameters, so that
all of them will be regulated dynamically by AIS. Since two extra AIS parameters (mi1, mi2) are required
for the update of one controller parameter pi, totally 2N AIS parameters are introduced in addition to the
ten parameters in the innate controller (described later).
The adaptive immunity brings about robustness against changes of operating conditions, leading to
enhanced system stability. This is achieved by optimal tuning of innate and adaptive controller parameters,
as elaborated in the following section.
7.4 AIS based oscillation damping controller
In this section, the development of an AIS-based adaptive controller for damping inter-area
oscillation in an interconnected power system is described. The flowchart for the development is given in
Figure 7.3 with details elaborated in the following subsections.
The following subsections describe the test power system used in this study, as well as the innate
and adaptive damping controller.
7.4.1 Innate damping controller
Traditional local PSS makes use of local generator speed deviations to generate a supplementary
control signal, which is superimposed on the voltage reference at the AVR of local generator. In this study,
local PSSs are designed based on H∞ based robust control approaches [12] (as detailed in Chapter 4) to
maintain power system stability. However, since poorly damped oscillations occur under critical operating
conditions, robust wide-area damping controllers are required.
84
Figure 7.3 Flowchart illustrating the development of an AIS based damping controller.
The innate damping controller is based on a VG-PSS introduced in Chapter 6 that makes use of
virtual generator speeds to generate a supplementary control signal at a generator of maximum
controllability, as shown in Figure 7.4. The methodology for tuning the VG-PSS parameters has been
elaborated in Chapter 6.
Start
Stop
Verification of damping effect for innate controller
Satisfactory?
Initialization of innate controller Parameters T0~T
5, K
1~K
4
PSO tuning of T0~T
5, K
1~K
4 with cost function
Verification of damping effect for AIS parameters
Initialization of AIS Parameters m1~m
20
PSO tuning of m1~m
20with cost function
Satisfactory?
Y
Y
N
N
85
Figure 7.4 Diagram of the proposed innate controller scheme.
In this approach, unlike H∞ based controller design that yields five high-order transfer functions
linking the five inputs and the output, the proposed innate controller has a simple mathematical expression
with only ten parameters, facilitating further approaches for adaptive parameter adjustments. The tuned
parameters are shown in Table I of Chapter 6. In the practice, this innate controller is installed at G9. The
method to compensate the time delay induced by data communication was successfully implemented in
earlier study in [13]. Recent researches also see the practice of using neural network based predictions to
overcome the time delay [49].
7.4.2 Adaptive damping controller
Based on the innate controller proposed, an AIS-based adaptive damping controller is developed as
shown in Figure 7.5. For each of the ten innate controller parameters, two extra AIS-parameters are
required. Thus, there are totally 20 AIS-parameters (m1 ~ m20) to be determined. The local speed deviation
Δω9 is used as the input for the AIS, thus the time delay is not considered by the adaptive damping
controller.
The stimulation and inhibition factors are determined through PSO approach, with the cost function
expressed in (7.5),
𝐾1
𝐾2
𝐾3
𝐾4
𝐾5
Σ 10𝑠
1 + 10𝑠𝐾0
𝑇1𝑠 + 1
𝑇2𝑠 + 1
𝑇3𝑠 + 1
𝑇4𝑠 + 1 𝐾𝐶 1 + 𝑠𝑇𝐶11 + 𝑠𝑇𝐶2
2
Δ 𝜔𝑉𝐺1
Δ 𝜔𝑉𝐺2
Δ 𝜔𝑉𝐺3
Δ 𝜔𝑉𝐺4
Δ 𝜔𝑉𝐺5
𝑉𝑜 0.1
−0.1 Washout Time-delay
compensator Limiter Lead-lag compensator
Generator Excitation
System
86
162
1 1( ( ))
N
ii j
J j
(7.5)
Where Δωi(j) is the speed deviation response of generator j at the moment of j. During the tuning of PSO,
each set of system parameters is represented as a particle. The ith particle is updated in terms of (7.6) and
(7.7),
, 0 , 1 1 , , 1 2 , 1( ) ( )i k i k i lbest i k gbest i kv v p p p p (7.6)
, 1 , ,i k i k i kp p v (7.7)
The cost function (7.5) only considers the time domain speed deviation responses. According to
Parseval’s theorem [50], the presence of any oscillation mode adds a positive value to J. Thus, the
optimization will enhance the damping for various oscillation modes.
The tuning process is carried out under simulation of 50ms three-phase faults at Bus 31. The power
system as well as the control circuit is simulated using RTDS; the delay block z-1 is realized via a first-
order holder with 10Hz sampling frequency. The PSO algorithm is implemented through MATLAB
programs, which interface RTDS with an RSCAD script. The tuned stimulation and inhibition factors are
indicated in Table 7.1.
The coordination of these two controllers is achieved by the consecutive tuning of innate and
adaptive controller. In response to oscillations following disturbances, with parameters adjusted by the
adaptive controller in the real time, the innate controller is able to provide a near-optimal supplementary
control signal at any moment, making the power system survivable under more critical operation
conditions.
87
7.5 Performance evaluation of AIS controller
The effectiveness of this adaptive controller with optimized parameters is verified through
simulation carried out on the RTDS. Three cases are studied corresponding to three different operating
conditions as well as contingencies, with different fault site, power generation and loading conditions. The
active power of each generator under these operating conditions are documented in the Table. A.2 in the
appendix. Compared with the study cases in [13], the active power transfer from NE to NY is higher, thus
the transmission lines linking these two subsystems are subject to heavier power flows, leading to easier
loss of oscillatory instability.
Table 7.1 Tuned stimulation and inhibition factors
m1 m2 m3 m4 m5 m6 m7
0.4495 -0.3506 -0.3514 0.0081 0.2286 0.4323 -0.0846
m8 m9 m10 m11 m12 m13 m14
-0.2564 -0.4868 0.3535 0.0894 -0.5 -0.2395 -0.4265
m15 m16 m17 m18 m19 m20
0.5 -0.0305 0.2578 -0.1623 0.2424 0.3076
Case I: The power system is operating under Operating Condition 1 (OC1), then a 50ms three-phase
fault happened at Bus 2, causing the transmission line connecting Bus 1 and Bus 2 to be tripped. The speed
responses of some selected generators are shown in Figure 7.6 when local PSSs are installed in G1-G12.
Without installation of innate controller, the oscillation amplitude increases with the time until loss of
synchronism. The innate controller is effective to maintain stability, while AIS-based adaptive controller
improves the damping effectiveness. A comparison of the damping ratio for each oscillation mode with
88
and without the designed controller is shown in Table 7.2. These damping ratios are calculated using
Prony Analysis [51].
Case II: With the transmission line from Bus 1 to Bus 2 already tripped, the system operating
condition change to OC2, then a 100ms three-phase fault happened at Bus 8. The speed responses of some
selected generators are shown in Figure 7.7 when local PSSs are installed in G1-G12. With only the local
PSSs, the power system quickly loses synchronism. With the installation of innate controller, the system
is marginally stable. With both the innate and adaptive controller, the system quickly recovers to steady
state. The comparison of the damping ratio for each oscillation mode with and without the designed
controller is shown in Table 7.2.
89
Figure 7.5 Schematic diagram of the AIS based controller.
𝛥𝜔9(𝑘)
𝛥𝜔9(𝑘 − 1)
×
×
𝐾0−𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑
𝐾1−𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑
𝐾5−𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑
𝑇𝐻𝑇1(𝑘)
𝑇𝑆𝑇1(𝑘)
𝑇1 𝑇1−𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑
𝐾2 𝐾3
𝐾4
𝐾5
Washout Time-delaycompensator Limiter
Lead-lagcompensator
Parameters
… …
… …
𝑧−1 ÷÷
exp(−𝑥2)
Σ
𝑚1 𝑇𝐻𝐾0(𝑘)
𝑚2 𝑇𝑆𝐾0(𝑘)
𝐾0 ++
-
++
-
++
-
++
-
++-
Σ
Σ
Σ
𝑚3 𝑇𝐻𝐾1(𝑘)
𝑚4 𝑇𝑆𝐾1(𝑘)
𝐾1
𝑚11 𝑇𝐻𝐾5(𝑘)
𝑚12 𝑇𝑆𝐾5(𝑘)
𝐾5
𝑚13 𝑚14
𝐾1
Σ10𝑠
1 + 10𝑠𝐾𝐶
1 + 𝑠𝑇𝐶11 + 𝑠𝑇𝐶2
2
Δ 𝜔𝑉𝐺1
Δ 𝜔𝑉𝐺2
Δ 𝜔𝑉𝐺3
Δ 𝜔𝑉𝐺4
Δ 𝜔𝑉𝐺5
𝑉𝑜0.1
−0.1
𝐾0
𝑇1𝑠 + 1
𝑇2𝑠 + 1
𝑇3𝑠 + 1
𝑇4𝑠 + 1
𝑚19 𝑇𝐻𝑇4(𝑘)
𝑚20 𝑇𝑆𝑇4(𝑘)
𝑇4 𝑇4−𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑
90
Figure 7.6 Speed responses of selected generators with local PSSs installation under Case I.
Local PSSs
Optimal Controller
Adaptive Controller
0 5 10 15 20-2
0
2
x 10-3
G1
0 5 10 15 20-202
x 10-3 G
5
0 5 10 15 20-2
0
2x 10
-3
speed d
evi
atio
n (
p.u
.)
G8
0 5 10 15 20-1
0
1x 10
-3 G10
0 5 10 15 20-1
0
1x 10
-3 G13
0 5 10 15 20-2
0
2x 10
-3
time (s)
G16
91
Figure 7.7 Speed responses of selected generators with local PSSs installation under Case II.
Local PSSs
Optimal Controller
Adaptive Controller
0 5 10 15 20
-2
02
x 10-3 G1
0 5 10 15 20
-2
02
x 10-3 G5
0 5 10 15 20
-2
02
x 10-3 G8
speed d
evia
tion (
p.u
.)
0 5 10 15 20-2
0
2x 10
-3 G10
0 5 10 15 20-2
0
2x 10
-3 G13
0 5 10 15 20-2
0
2x 10
-3 G16
time (s)
92
Figure 7.8 Speed responses of selected generators with local PSSs installation under Case III.
Case III: System operating conditions change to OC3, then a 100ms three-phase fault happened at
Bus 27. Compared with OC2, there is an increase of active power transfer from New England to New
York, and the load at Bus 1 has increased by 100%. The speed responses of some selected generators are
shown in Figure 7.8 with local PSSs installation on G1-G12. With only the innate controller, power system
loses stability following the disturbances. However, the power system is stabilized with the installation of
0 5 10 15 20
-202
x 10-3 G1
0 5 10 15 20-2
0
2
x 10-3 G5
0 5 10 15 20-2
0
2
x 10-3 G8
speed d
evia
tion (
p.u
.)
0 5 10 15 20-2
0
2x 10
-3 G10
0 5 10 15 20-2
0
2x 10
-3 G13
0 5 10 15 20-2
0
2x 10
-3 G16
time (s)
Innate Controller
Adaptive Controller
93
both innate and adaptive controller. The comparison of the damping ratio for each oscillation mode with
and without the designed controller is shown in Table 7.2.
Figure 7.9 Deviation of parameters with time for all three case studies (Case I, II & III).
The deviation of the innate controller parameters with respect to time under the three cases described
above are shown in Figure 7.9.
Case I
Case II
Case III
0 5 10 15
-0.4-0.2
00.2
K1
0 5 10 15-0.4-0.2
00.20.4
K2
0 5 10 15
-0.5
0
0.5
K3
0 5 10 15-0.2
0
0.2
K4
0 5 10 15-0.4-0.2
00.20.4
K5
Change o
f P
ara
mete
rs
0 5 10 15-1
0
1
K0
0 5 10 15
-0.2
0
0.2
0.4
T1
0 5 10 15
-0.5
0
0.5
T2
0 5 10 15
-0.2
0
0.2
Time (s)
T3
0 5 10 15-0.5
0
0.5
Time (s)
T4
94
Table 7.2 Damping ratio for different modes under Case I – III
Cases Cases 0.22 Hz 0.42 Hz 0.54 Hz 0.65 Hz
Only with local PSSs
Case I -2 % 12.6% 7.3% 6.9%
Case II Unstable
Case III Unstable
With innate controller
Case I 9.1 % 15.2% 11.2% 12.4%
Case II 3 % 14.1% 10.2% 11.9%
Case III Unstable
With adaptive controller
Case I 14.6 % 17.1% 13.5% 13.1%
Case II 15.6 % 16.1% 14.5% 13.6%
Case III 14.7 % 16.3% 13.9% 14.4%
7.6 Summary
This study has proposed an AIS-based wide area adaptive damping controller that uses virtual
generator speeds for supplementary control signal to mitigate inter-area oscillations in a power system.
The control is carried out at the generator of maximum controllability identified through modal analysis.
The optimal tuning of controller parameters provides innate immunity, while adaptive immunity is
available by a mechanism to adjust controller response policy according to the measured disturbance. The
parameters of innate and adaptive controllers are tuned by particle swarm optimization. As verified by
simulations on RTDS, the proposed AIS based controller is able to stabilize the power system under
different disturbances, and achieve better performance under various operating conditions.
95
CHAPTER 8
WIDE-AREA MEASUREMENT BASED MULTI-OBJECTIVE SMARTPARK
CONTROLLERS FOR A POWER SYSTEM WITH A WIND FARM
8.1 Introduction
The integration of variable generation such as wind and solar power has brought about
significant challenges and uncertainty in power system operation, making it essential to take
measures for advanced coordinated control. With the batteries of plug-in electrical vehicles (PEVs),
active and reactive power support functions can be provided at certain buses in a power system.
Parking lots with a large number of PEVs, referred to as SmartParks, can provide these functions
at bulk level. Thus, by appropriate control of SmartParks, active and reactive power flows in a
power system can be regulated to achieve the functionalities of oscillation damping control,
transmission line power flow regulation and bus voltage control. In this paper, in order to realize
these three functionalities concurrently by using SmartParks, fuzzy-logic based controllers are
proposed. Wide area measurements from a power system can be used to generate the active and
reactive power output dispatch command signals for SmartParks. The parameters of the fuzzy logic
controllers are heuristically determined to provide optimal system-wide performances for
oscillation damping, transmission line power flow regulation and bus voltage control. Typical
results are provided on a 12-bus power system with 400 MW wind farm implemented on a real-
time simulation platform.
8.2 Problem formulation
Nowadays, as Plug-in-Vehicles (PEVs) are increasingly being applied in power systems, the
battery of PEVs can participate in power system control [52]-[54]. A SmartPark is a PEV parking
96
lot capable of vehicle-to-grid (V2G) and grid-to-vehicle (G2V) transactions. The cumulative
battery energy storage of the PEVs has the capability to provide active and reactive power
injections into a power system [55]. It can be assumed that a predictable amount of PEVs are
present in the SmartPark connected to the power grid during day and night such as university
parking lots and airport parking lots. Meanwhile, due to the variable nature of renewable sources
of energy such as wind and solar power, increasing levels of penetration can cause fluctuation of
bus voltages and power flows in the transmission system. In the predictable future, the batteries of
PEVs can be used to mitigate the fluctuations caused by large integration of wind and solar power
sources.
Previous research has explored various applications of SmartParks in power system control. In
[56], SmartPark is deployed as a shock absorber to maintain constant active power flows in
transmission lines connected to a wind farm. Active power is absorbed or injected by a SmartPark
to compensate for a change in a wind farm output. However, this functionality can be effective
only if a SmartPark is in proximity to a wind farm. Coordinated control based on remote
measurements is needed when SmartParks are distant from wind farms. In [57], to provide bus
voltage regulation, a SmartPark has been utilized as a virtual STATCOM to provide reactive power
compensation. Herein, local bus voltage measurements are used to control the SmartPark’s
reactive power dispatch. However, voltage support of adjacent buses have not been explored. The
impact of SmartPark on adjacent buses has not been shown. The application of SmartPark for
oscillation damping controller has been studied in [58]. The difference of the generator speeds and
the state of charge of the SmartPark are used as inputs to a fuzzy logic based controller. The fuzzy
controller determines the amount of SmartPark active power to be dispatched in order to enhance
the damping torque. The above mentioned studies have focused on individual applications of
97
SmartPark capabilities. However, for maximum utilization of SmartPark resources for control of
power systems, it is desired that all these capabilities be tapped concurrently. Furthermore,
SmartParks installed at different locations/buses need to be coordinated for enhanced system-wide
performance. This requires wide-area power system measurements and intelligent coordinated
control.
In this paper, the multi-functionality of SmartParks through a coordinated approach to achieve
three objectives, namely, i) power oscillation damping control, ii) transmission line power flow
control and iii) voltage regulation, is investigated. This multi-functionality is studied on a power
system with wind power fluctuations. In order to realize these objectives, an intelligent coordinated
control is needed to dispatch active and reactive power from the SmartPark(s) in real time. The
intelligent control of SmartPark inverters is based on wide-area power system measurements such
as generator speed deviations, transmission line power flows and bus voltages.
The overall diagram to implement the above mentioned multi-functional control of SmartParks
is shown in Figure 8.1. Two control loops are implemented. Using the decoupled d-q axis current
control, the inner control loop provides a reference tracking control for the active and reactive
power dispatches and this is fast-responding control action. The outer loop makes use of wide-area
system measurements to generate the active/reactive power reference signals to the inner control
loop. This is slower in response compared to the inner control loop. The inner control loops
developed in [57] can achieve satisfactory active/reactive power reference tracking. Therefore, this
study is focused on the development of outer loop control to achieve the three objectives mentioned
above. Due to the nonlinearity of power system and the unknown relationship between the
controller’s multiple inputs and multiple outputs, a Tagaki-Sugeno type fuzzy logic controller is
proposed instead of traditional controllers such as PI controllers and lead-lag compensators. To
98
develop an optimal fuzzy controller, a system-wide fitness function that reflects the three
objectives is used to determine the parameters of the controller. With optimal controller parameters
determined offline, an overall satisfactory power system performance can be realized under
disturbances for various operating conditions including different wind speeds.
99
Figure 8.1 The overall diagram for the SmartPark control scheme
PSP2, QSP2PSP1
Pulses Pulses
𝛥 Pref
𝛥𝑃16 − 𝛥𝑃64 𝛥𝑉4
𝛥 Qref
Inner control loop Inner control loop
IMFC_1 / IMFC_1' IMFC_2 / IMFC_2'
SmartPark 1 SmartPark 2
12 Bus Power System Bus 6 Bus 4
Switch 1 Switch 2
𝛥𝑃64 Σ
𝑉4
𝑉4,ref
+
𝛥𝜔2 − 𝛥𝜔3
Σ 𝛥𝜔2
𝛥𝜔3
+
− −
𝛥𝑃16 − 𝛥𝑃64
Σ 𝑃16
𝑃16,ref
Σ
𝛥𝑃16
Σ 𝑃64 𝑃64,ref
+
+ +
+
−
−
PMUs
Mea
sure
men
ts
𝑃wind, 𝑛𝑜𝑟𝑚𝑖𝑛𝑎𝑙
𝛥 Pref
Σ Σ
+
+ 𝑃wind
Σ +
− Pref
Ptotal
SP-DC
100
8.3 Power system with a wind farm and SmartParks
8.3.1 12-BUS FACTS benchmark test power system
Shown in Figure 8.2 is the 12-bus FACTS benchmark test power system used in this study, it
consists of three voltage levels (as labeled in Figure 2) and is divided into three areas [59]. G1 is
a representation of an infinite power system, thus the voltage amplitude and angle at Bus 9 is
regarded to be constant. G2 and G3 are synchronous generators; thus, during power system
transients, the rotation speed of G2 and G3 are subject to fluctuations. G4 at Bus 6 is a
representation of a wind farm with a DFIG model, which is further connected with Bus 1 and Bus
4 through two transmission lines. Bus 4 is the major load bus with the lowest voltage profile, and
is subject to large fluctuation following disturbances.
As the output of wind farm changes, the active power flow in the power system is subject to
variations, leading to possible exceeding of power flow constraints in transmission lines.
Following contingencies, oscillations are exhibited through speed deviations of G2 and G3,
leading to possible loss of synchronism.
Figure 8.2 12-bus power system
101
8.3.2 Wind farm model
As a variable generation source, a Doubly Fed Induction Generator (DFIG) based wind farm
is used in this study. The stator side and rotor side of the DFIG are connected to a DC-link capacitor
through a Grid Side Converter (GSC) and a Rotor Side Converter (RSC) respectively. In the wind
farm, with a d-q decoupled control method, the active power output of the DFIG can be regulated
to realize maximum power point tracking through control of RSC; while the DC voltages as well
as the DFIG reactive power output can be regulated through control of GSC. Detailed modeling
of a DFIG is given in [60]. In this study, the output of the wind farm varies as the wind speed
changes, and thus leads to variation of transmission lines power flows. Variation of wind speeds
causes the change of the active power output of G4, therefore it impacts the power flow of the
whole power system. Control actions are required to maintain the transmission line flows.
8.3.3 SmartPark model
A graphical representation of a SmartPark model is shown in Figure 8.3. The battery of the
PEV can be modeled as a DC voltage source connected with a three phase inverter, and ultimately
linked with the power system through an inductance. The DC voltage is 307V at 50% state of
charge; the inductance in series is 0.005Ω, while the rms line-to-line voltage of inverter output is
208V [57]. Assuming a constant grid voltage, the amplitude and phase of the inverter side voltage
is regulated through pulses for the six fast switches to regulate, and thus the active and reactive
power injected to the power grid can be impacted. In operations, it is generally required that the
active and reactive power output of the SmartPark tracks a reference value. To realize this, as
indicated in Figure 8.4, is the inner control loop for generation of pulses. For the convenience of
analysis, the current in the rotating a,b,c phases are transformed to a stationary d-q-axis system.
The equivalent current iqs is in phase with the grid voltage and is closely related to the active power
102
output of the SmartPark, while the equivalent current ids is 90 degrees lagging the grid voltage and
is closely related to the reactive power output [61]. Thus, the output voltage can be expressed in a
phasor form as C CV V . Large amount of active power delivery by the batteries corresponds
to a higher phase angle α; while large amount of reactive power delivery corresponds to higher
voltage level |V|.
Figure 8.3 Schematic circuit representation of a SmartPark
Figure 8.4 The inner control loop for SmartPark
In this control scheme, the references for iqs and ids are given by (8.1) and (8.2) in terms of
active and reactive power references (namely P* and Q*) respectively. The integrators in Figure
4 guarantee that P and Q reach their reference values in steady states.
*
* *2 d3qs
peak
Pi K P P tv
(8.1)
103
*
* *2 d3ds
peak
Qi K Q Q tv
(8.2)
The total actual active and reactive power output can be expressed in (8.3) and (8.4), and can
be directly measured.
3 ( )2 qs qs ds dsP v i v i (8.3)
3 ( )2 qs ds ds qsQ v i v i (8.4)
For each phase, the current reference value is compared with the actual values; their differences
are modulated to generate inverter pulses corresponding to each specific case. According to
previous research, due to the fast switching characteristics of the IGBTs that comprises the
SmartPark circuit, it can be seen that the actual active/reactive power generation by SmartParks
almost overlaps with the reference values [56].
The state of charge (SOC) is a reflection of fuel gauge for PEV batteries. The SmartPark
functionalities cannot be realized under excessively high or low value of SOC. Generally, the
charging or discharging of batteries corresponds to a positive or negative active power generated
by the SmartPark, leading to the change of SOC. Fortunately, the functionality of SmartPark as
damping controller only involves the SmartPark active power output in a short transient process,
and has little impact on the SOC. Since the wind speed is generally changing around the nominal
value, there is both positive and negative amount of active power output of SmartPark as a
transmission line active power regulator, the net effect of charging and discharging is to maintain
the SOC value to a proper range. SmartPark as a voltage regulator mainly involves the reactive
power output, and has negligible impact on the SOC.
All these issues related damping oscillations, voltage regulation and power flow regulation
require a coordinated intelligent multi-functional control which is addressed in the next section.
104
8.4 Development of an intelligent multi-functional controller (IMFC) for SmartParks
So far, with the main circuit and the inner loop controller elaborated above, a SmartPark is able
to track its active and reactive power references during operation. An outer-loop controller is
required to generate these references from the power system measurements. There are many
traditional methods for development of controllers. Such as H∞-based approaches [62], [63].
However, in an interconnected power system, relationships between measurements (including
speed deviations of generators, transmission line power flows, and voltage deviations at buses)
and active/reactive power references of a SmartPark are unknown. Besides, conventional power
system models are subject to a lot of constraints including nonlinearity, time-dependence and
stochastic nature of power systems. In this study, instead of using traditional control approaches,
a Takagi-Sugeno type fuzzy network based IMFC is developed to generate the reference signals
to a SmartPark. The structure of a Takagi-Sugeno type fuzzy network provides a nonlinear
mathematical relationship between the input and output signals. The parameters of the fuzzy
network can be heuristically determined to provide optimal SmartPark and power system
performance. During the development of this controller, power system measurements that provide
the most observability to achieve the objectives are used as the inputs to the SmartPark. The
oscillatory stability can be best observed from the speed deviations of the generators as well the
voltage profiles at selected buses. The power flow regulation can be observed directly from
transmission line power flow measurements. The voltage regulation can be observed directly from
the voltage profiles measured at the respective buses.
The following three objectives of the multi-functional control can be realized as follows:
i. An improved oscillation damping performance can be achieved by an increased
damping ratio in the speed deviation responses of generators and transmission line
105
power flows. As a result the generator speed deviation responses and/or transmission
line power flows can be used as inputs of an IMFC which in turn can generate changes
to the active power reference command to a SmartPark.
ii. The transmission line power flows deviations from their nominal values can be used to
generate an active power reference command to a SmartPark to regulate transmission
line power flows.
iii. The voltage profile at crucial buses can be directly measured to generate a reactive
power reference command to a SmartPark to regulate voltage levels at respective buses.
The above mentioned objectives to enhance power system operational performance are
illustrated with two SmartParks having secondary controllers (IMFC_1 and IMFC_2) as shown in
Figures 8.1 and 8.2. SmartPark 1 realizes the first two of three functionalities concurrently.
SmartPark 2 realizes the last two of three functionalities concurrently.
8.4.1 Tagaki-Sugeno fuzzy network (TSFN)
Indicated in Figure 5 is a schematic diagram of a Tagaki-Sugeno Type fuzzy network. It is
composed of several layers [64], [65]. In Layer 1, each of the input channels is propagated through
nonlinear functions to form the inputs of Layer 2. Suppose there are M inputs, and each input has
connections with N nonlinear membership (Gaussian) functions; thus, Layer 2 has totally MN
inputs. Each element of Layer 3 is the product of several Layer 2 members connected to different
elements of Layer 1. Thus, there are R=NM product functions in Layer 3. Each element of Layer 4
(output layer) is a linear weighed sum of Layer 3 outputs. It is worth noting that an offset is added
to each output node in order to guarantee that zero inputs lead to zero outputs for initialization.
The formulae of this mathematical formulation is shown in (8.5).
106
1
2, 2, 1,
3, 2,
'4, 3,
1'4, 4,
(
);
;
.
; 1,2...
N
i i j
p
k pp p
R
m k kk
m m m
l f l
l l
l c l
l l d m K
(8.5)
in which K is the number of outputs, md is the offset that corresponds to the value of l’4,m under
zero-inputs. The function of this deviation is to guarantee that control signals decay to zero
whenever the power system restores to its original steady state. The nonlinear membership
functions f2,i() can be realized through various analytic mathematical forms. In this study, Gaussian
functions with the expressions in (8.6) are adopted.
2 2( ) /(2 )( ) x b cf x ae (8.6)
(a) (b)
Figure 8.5 The structure of IMFCs
(a) TKFN for IMFC_1 and (b) TKFN for IMFC_2.
There are two parameters in each of the MN Gaussian membership functions; meanwhile,
there are NM parameters of ck ’s in the output layer. Thus, (2MN + KNM) parameters are present in
TSFN controller. To guarantee that the controller generates correct signals for better control
107
effectiveness, it is essential to optimally configure these parameters. Herein, a heuristic
optimization method, namely, Mean Variance Optimization (MVO) is applied [68]. MVO
iteratively determines the system parameters for minimization of an objective function, as
elaborated in the following subsection.
8.4.2 MVO based TSFN parameter tuning
The TSFN parameters can be heuristically configured to achieve the objectives of IMFCs.
Traditionally, heuristic algorithms like particle swarm optimization, MVO and genetic algorithm
are used for tuning of controller parameters [66]-[69]. In this study, MVO is used to tune the TSFN
parameters for minimization of an objective function that is obtained through simulations. In each
iteration, the MVO assigns new values to a chosen number of parameters in the best individual
according to the distribution characteristics of the parameters such as the mean and the variance
value, which are calculated through a list of the best N individuals that are evaluated. The
relationship of old and new value of the parameter can be expressed in (8.7),
(1 )(1 ) (1 ) ( 1 )old oldx s x s snew oldx x e x e e x x (8.7)
where ln( ) ss v f ; x and v are the mean and variance of that parameter respectively; fs is a shaping
scaling factor.
The list of best N individuals is constantly being updated whenever a better solution is found.
In the next iteration, a different set of parameters are subject to mutation.
The objective function serves as an evaluation of the system performance, and is calculated
through simulated measurements such as speed deviation, voltage as well as transmission line
active power flows. As elaborated in the following subsections, in order to achieve an IMFC, the
overall objective function can be expressed as the weighted sum of the three individual objectives.
The selection of weights needs to consider the importance for each objective, as well as the
108
calibration for different numerical scales. In case more than one TSFN controller is installed in a
power system, the parameters of all the TSFN controllers can be concurrently optimized. The
development of IMFCs for two SmartPark installations is investigated in this study via three case
studies.
8.4.3 Development of IMFC for SmartPark installation at Bus 6
An IMFC is developed for SmartPark installation Bus 6 to damp generator oscillations and
mitigate active power fluctuations caused by wind speed changes. This controller, referred to as
‘IMFC_1’ is shown in Figures 1 and 5a. Switch 1 turned on connects SmartPark 1 to Bus 6.
Without the SmartPark, significant difference of speed deviation of generators G2 and G3
(Δω2−Δω3) can be observed. Besides, the variation of active power output of the wind farm
(ΔPwind), is accompanied by the difference of the active power flow deviation, (ΔP16−ΔP64), of the
two transmission lines, namely, lines 1-6 and 6-4, as expressed in (8.8),
ΔPwind = −(ΔP16−ΔP64) (8.8)
Thus, two inputs are selected for IMFC_1, namely, i) the difference between speed deviations
of generators G2 and G3, (Δω2−Δω3) and ii) the difference of the active power flow deviation, −
(ΔP16−ΔP64). The output of the IMFC_1 is the active power output reference command to the
SmartPark 1, PSP1. Each input is connected to five Gaussian membership functions, thus totally
there are 45 (2MN + KNM =2×5×2+52 ) parameters. The ability of the SmartPark as an active power
source is based on the battery energy storage. Under this control, the increase of the wind power
output is accompanied by the charging of the battery; while the decrease of the wind power output
is accompanied by the discharging of the battery. Thus, the variation of wind speed brings about
alternating battery charging and discharging process, and maintains the SOC between some
minimum and maximum levels.
109
In each iteration of MVO based parameter configuration, three events were taken for the
verification of the control effectiveness: (i) three phase faults at Bus 6 is applied, the speed
deviations of G2 and G3 are measured; (ii) increase in wind speed, active power flow on
transmission line Bus 1-Bus 6 and Bus 6-Bus 4 are measured. (iii) decrease in wind speed, active
power flow on transmission line Bus 1-Bus 6 and Bus 6-Bus 4 are measured. The cost function
used by MVO for determining the TSFN parameters is given in (8.9),
1 2 3
2 2 2 2 2 21 2 1 3 1 1 16 2 64 2 16 3 64 3( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( ))
t t tJ t t P t P t P t P t
(8.9)
where t1 corresponds to a time window after the fault; t2 corresponds to a time window following
the wind speed increase; while t3 corresponds to a time window following the wind speed decrease.
8.4.4 Development of IMFC for SmartPark installation at Bus 4
In this case, an IMFC is developed for SmartPark installation Bus 4 for voltage regulation and
to mitigate active power fluctuations caused by wind speed changes. The structure of this controller,
referred to as ‘IMFC_2’ has been shown in Figure 1 and Figure 5b. Switch 2 turned on connects
SmartPark 2 to Bus 4. Since the voltage of Bus 4 can be directly measured, the voltage deviation
(ΔV4=V4−Vstandard) is taken as the one of the input for the IMFC_2. Like the previous subsection,
the difference of the active power flow deviation of the two transmission lines (ΔP16−ΔP64) is
taken as the other output, since it is a reflection of the wind farm output impact on the transmission
line active power flow. The outputs of this controller are the active and reactive power output
reference commands to SmartPark 2. This controller has a total of 48 parameters. Each input is
connected to four Gaussian membership functions, thus totally there are 48 (2MN + KNM
=2×4×2+2×24) parameters.
110
In each iteration of the MVO based parameter search, three events were taken for the
verification of the control effectiveness: (i) three phase faults at Bus 4 is applied, the speed
deviations of G2 and G3 are measured; (ii) increase in wind speed, active power flow on
transmission line Bus 4-Bus 5 and Bus 4-Bus 3 are measured; (iii) decrease in wind speed, active
power flow on transmission line Bus 4-Bus 5 and Bus 4-Bus 3 are measured. The cost function
used by MVO is expressed in (8.10),
1 2 3
2 2 2 2 22 4 1 2 45 2 43 2 45 3 43 3( ( )) ( ( )) ( ( )) ( ( )) ( ( ))
t t tJ V t P t P t P t P t
(8.10)
where t1 corresponds to a time window after the fault; t2 corresponds to a time window following
the wind speed increase; while t3 corresponds to a time window following the wind speed decrease.
It is illustrated in Section 4 that the increase and decrease of the wind power output is accompanied
by reverse effects of battery charging and discharging. Thus, the alternating increase and decrease
of wind speed leads to the maintenance of SOC between some minimum and maximum levels..
8.4.5 Development of IMFC for SmartPark installation at Bus 4 and 6
In this case, it is desired that a constant power flow is maintained at the four transmission lines
(Bus 1-Bus 6, Bus 6-Bus 4, Bus 4-Bus 3, Bus 4-Bus 5), the voltage profile near load buses be
maintained, and damping torque is provided to better maintain phase angle stability of G2 and G3.
Thus, two IMFCs are concurrently installed at Buses 4 and 6. These implies switches 1 and 2 in
Figure 1 are turned on connecting SmartPark 1 and 2 to Buses 6 and 4, respectively. The
parameters of the two IMFCs designed in Section 3.3 and 3.4 are taken as the initial parameters, a
total of 93 parameters. Thereafter, these 93 parameters are further tuned with MVO according to
the cost function as expressed in (8.11),
111
1
1
2 3
2 21 2 1 3 1
22 4 1
2 2 2 2 2 2 2 23 16 2 64 2 45 2 43 2 16 3 64 3 45 3 43 3
3 1 3 2 3 3
( ( )) ( ( ))
( ( ))
( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( ))
t
t
t t
J t t
J V t
J P t P t P t P t P t P t P t P t
J J J J
(8.11)
where t1 corresponds to a time window after the fault; t2 corresponds to a time window following
the wind speed increase; while t3 corresponds to a time window following the wind speed decrease.
The concurrently tuned IMFC controllers at Buses 4 and 6 are referred to as ‘IMFC_1' ’ and
‘IMFC_2' ’ respectively.
8.5 Simulation results
Shown in Figure 8.6 is controller flowchart for the developing the IMFCs using MVO.
112
Figure 8.6 The flowchart for development of IMFC
To verify the effectiveness of the proposed controllers, (IMFC_1, IMFC_2, IMFC_1' and
IMFC_2'), simulations are carried out on a 12-bus power three-area system [59]. Several different
simulation cases are presented in the following subsections. The fuzzy logic controller
implementation is realized through a C code based block that is embedded as an RTDS component.
The calculation of the objective function for each MVO iteration is via a simulation on a Real
Time Digital Simulator (RTDS). The MVO algorithm is implemented using MATLAB, which
interacts with RTDS platform using the RSCAD script files. Once the fuzzy controller parameters
are configured through MVO, the controller development is accomplished.
Case 1: SmartPark installation at Bus 6
Start
MVO tuning of TKFN parameters for SmartPark installation at Bus 6
Design of inner loop controller of SmartPark
MVO tuning of TKFN parameters for SmartPark installation at Bus 4
Secondary MVO tuning of TKFN for SmartPark installation at Bus 4 and Bus 6
End
Performance verification
Satisfactory ?
Y N
Development of TKFN structure
113
In this case, the parameter tuning algorithm takes approximately 400 MVO iterations to
converge. With the optimally configured parameters, the damping effectiveness of this control
method is presented by post-fault generator speed deviations. The simulation result is compared
with a prior study where a SmartPark with a Difference Controller (SP-DC) is used. The SP-DC
controller calculates the active power output reference of the SmartPark as the difference between
the wind farm active power output under nominal wind speed (12 m/s) and the actual wind farm
active power output [56].
Indicated in Figure 8.7 are the speed deviations of G2 and G3 following a 100ms three phase
fault at Bus 6 for wind speed of 12 m/s, 15 m/s and 10 m/s. It can be seen that IMFC_1 enables
the SmartPark 1 to inject active power into Bus 6 to damp generator speed oscillations more
effectively compared with the previously developed SP-DC controller. This is seen from the
damping ratios shown in as Table I.
114
Figure 8.7 The speed deviations of G2 and G3 following a 100ms three phase fault at Bus 6.
(a) Speed deviation at G2 with wind speed of 12 m/s; (b) Speed deviation at G2 with wind speed of 15 m/s;(c) Speed deviation at G2 with wind speed of 10 m/s; (d) Speed deviation at G3 with wind speed of 12 m/s;(e) Speed deviation at G3 with wind speed of 15 m/s; (f) Speed deviation at G3 with wind speed of 10 m/s.
Table 8.1 Damping ratios of speed deviation responses
Condition Damping Ratio
Wind speed of 12 m/s Wind speed of 15 m/s Wind speed of 10 m/s
No SmartPark 7.1% 5.5% 3.5%
SP_DC 9.2% 8.2% 8.1%
IMFC_1 16.0% 13.5% 16.5%
Illustrated in Figure 8.8 are the active power flows on transmission lines Bus 1-Bus 6 and Bus
6-Bus 4 following a change in wind speed. It can be seen that the proposed controller achieves
4 6 8 10 12
-1
0
1
x 10-3
Speed d
ev (
p.u
.)
(a)
Time (s)
No SmartPark
SmartPark with SP-DC
SmartPark with IMFC_1
4 6 8 10 12
-1
0
1
x 10-3
Speed d
ev (
p.u
.)
(b)
Time (s)
4 6 8 10 12
-5
0
5
x 10-4
Speed d
ev (
p.u
.)
(c)
Time (s)
4 6 8 10 12-5
0
5x 10
-3
Time (s)
Speed d
ev (
p.u
.)
(d)
4 6 8 10 12-6
-4
-2
0
2
4
6x 10
-3
Time (s)
Speed d
ev (
p.u
.)
(e)
4 6 8 10 12-1.5
-1
-0.5
0
0.5
1
1.5x 10
-3
Time (s)
Speed d
ev (
p.u
.)
(f)
115
comparable effectiveness for regulating transmission line power flows, with some improvements.
The active power output of the SmartPark 1 is shown in Figure 8.9. It can be seen that, the increase
and decrease of wind speed can lead to opposite trends of battery charging or discharging.
Figure 8.8 The active power flows on transmission lines following wind speed changes.
(a) Active power from Bus 1 to Bus 6 with wind speed change from 12 m/s to 15 m/s;(b) Active power from Bus 1 to Bus 6 with wind speed change from 12 m/s to 10 m/s.(c) Active power from Bus 6 to Bus 4 with wind speed change from 12 m/s to 15 m/s;(d) Active power from Bus 6 to Bus 4 with wind speed change from 12 m/s to 10 m/s;
0
100
200
(a)
No SmartPark
SmartPark with SP-DC
SmartPark with IMFC_1
100
200
300
(b)
0 5 10 15 20175
180
185
Active
Pow
er(
MW
)
Time (s)0 5 10 15 20
175
180
185
Active P
ow
er
(MW
) Time (s)
50
100
150
Active P
ow
er
(MW
)
(c)
0
50
100
Active P
ow
er
(MW
)
(d)
0 5 10 15 2076
77
78
Time (s)
0 5 10 15 2076
77
78
Time (s)
116
Figure 8.9 The active power output of the SmartPark 1 for Case 1. (Under wind speed of 12
m/s)
Case 2: SmartPark installation at Bus 4
In this case, the parameter tuning algorithm takes approximately 300 MVO iterations to
converge. With the optimally configured parameters, the damping effectiveness of this control
scheme is presented by the post-fault generator speed deviations. Shown in Figure 8.10 are the
voltage profile of selected buses that are close to a major load. It can be seen that the voltage profile
is improved, and quickly settles to steady state with the proposed IMFC_2.
0 5 10 15 20-200
-150
-100
-50
0
50
Time (s)
Active P
ow
er
(MW
)
0 5 10 15 20-50
0
50
100
150
200
Time (s)
Active P
ow
er
(MW
)
0 5 10 15 20-150
-100
-50
0
50
100
Time (s)
Active P
ow
er
(MW
)
117
Figure 8.10 The voltage profile of selected buses.
(a) Voltage at Bus 4 with wind speed of 12 m/s; (b) Voltage at Bus 4 with wind speed of 15 m/s;(c) Voltage at Bus 4 with wind speed of 10 m/s; (d) Voltage at Bus 5 with wind speed of 12 m/s.(e) Voltage at Bus 5 with wind speed of 15 m/s; (f) Voltage at Bus 5 with wind speed of 10 m/s.
Shown in Figure 8.11 are the active power flows on transmission lines Bus 4-Bus 5 and Bus
4-Bus 3 following a change in wind speed. It can be seen that the proposed IMFC_2 is effective in
regulating the transmission line power flows. The active and reactive power output of the
SmartPark 2 is shown in Figure 8.12. Likewise, it can be seen that, the increase and decrease of
wind speed can lead to opposite trends of battery charging or discharging.
0.8
0.9
1
Vol
tage
(p.
u.)
(a)
Time (s)
No SmartPark
SmartPark with IMFC_2
0.8
0.9
1
Vol
tage
(p.
u.)
(b)
Time (s)
0.8
0.9
1
Vol
tage
(p.
u.)
(c)
Time (s)
4 6 8 10 120.9
0.95
1
1.05
1.1
Time (s)
Vol
tage
(p.
u.)
(d)
4 6 8 10 120.9
0.95
1
1.05
1.1
Time (s)
Vol
tage
(p.
u.)
(e)
4 6 8 10 120.9
0.95
1
1.05
1.1
Time (s)
Vol
tage
(p.
u.)
(f)
118
Figure 8.11 The active power flows on transmission lines following wind speed changes.
(a) Active power from Bus 3 to Bus 4 with wind speed change from 12 m/s to 15 m/s;(b) Active power from Bus 3 to Bus 4 with wind speed change from 12 m/s to 10 m/s.(c) Active power from Bus 5 to Bus 4 with wind speed change from 12 m/s to 15 m/s;(d) Active power from Bus 5 to Bus 4 with wind speed change from 12 m/s to 10 m/s;
0 5 10 15 20140
160
180
200
Active p
ow
er
(MW
)
(a)
Time (s)
No SmartPark
SmartPark with IMFC_2
0 5 10 15 20
160
180
200
220
Active p
ow
er
(MW
)
(b)
Time (s)
0 5 10 15 2010
20
30
40
Time (s)
Active p
ow
er
(MW
)
(c)
0 5 10 15 2020
30
40
50
Time (s)
Active p
ow
er
(MW
)
(d)
119
Figure 8.12 The active power and reactive output of the SmartPark for Case 2.
(a)Active Power output for wind speed increase; (b) Reactive Power output for wind speed increase(c)Active Power output for wind speed decrease; (d)Reactive Power output for wind speed decrease
(e)Active Power output following a fault; (f) Reactive Power output following a fault
Case 3: SmartPark installations at Bus 4 and Bus 6
In this case, the parameter tuning algorithm takes approximately 300 iterations to converge.
With the optimally configured parameters, the damping effectiveness of this control method is
presented by the post-fault generator speed deviations. The effectiveness of the proposed
controllers (IMFC_1' and IMFC_2') is compared with that of previously developed controller in
[56], as well as with the case of no controller. Shown in Figure 8.13 are the speed deviations of
G2 and G3 and the voltage profile at Bus 4 and Bus 5 following a 100ms three phase fault at Bus
6 under nominal wind speed of 12 m/s. It can be seen that, with the proposed IMFC controllers,
the damping effectiveness and the voltage profile are with the best performances.
-100
-50
0
50
Active p
ow
er
(M
W)
(a)
Time (s)-50
0
50
Rective p
ow
er
(M
VA
R)
(b)
Time (s)
0
50
100
Active p
ow
er
(M
W)
(c)
Time (s)-20
-10
0
10
Rective p
ow
er
(M
VA
R)
(d)
Time (s)
0 5 10 15 20-100
0
100
200
Time (s)
Active p
ow
er
(M
W)
(e)
0 5 10 15 20-50
0
50
100
Time (s)
Rective p
ow
er
(M
VA
R)
(f)
120
Figure 8.13 Power system measurements following a 100ms three phase fault at Bus 6.
(a)Speed deviation at G2; (b) Speed deviation at G3; (c) Voltage at Bus 4; (d) Voltage at Bus 5.
Shown in Figure 8.14 are the active power flows on the four transmission lines following
change in wind speeds. It can be seen that the proposed controllers achieve comparable
effectiveness for regulating transmission power flows, with some improvements.
4 6 8 10 12
-1
-0.5
0
0.5
1
x 10-3
Spe
ed d
ev. a
t G2
(p.u
.)
(a)
Time (s)
No SmartPark
SmartPark with SP-DC
SmartPark with SmartPark with IMFC_1' and IMFC_2'
4 6 8 10 12-5
0
5x 10
-3
Spe
ed d
ev. a
t G3
(p.u
.)
(b)
Time (s)
4 6 8 10 120.96
0.98
1
1.02
Vol
tage
at B
us 4
(p.u
.)
(c)
Time (s)
4 6 8 10 121
1.02
1.04
1.06
1.08
Time (s)
Vol
tage
at B
us 5
(p.u
.)(d)
121
Figure 8.14 The active power flows on transmission lines following wind speed changes.
(a) Active power transfer from Bus 1 to Bus 6 subjected to wind speed change from 12 m/s to 15 m/s(b) Active power transfer from Bus 1 to Bus 6 subjected to wind speed change from 12 m/s to 10 m/s(c) Active power transfer from Bus 6 to Bus 4 subjected to wind speed change from 12 m/s to 15 m/s(d) Active power transfer from Bus 6 to Bus 4 subjected to wind speed change from 12 m/s to 10 m/s(e) Active power transfer from Bus 3 to Bus 4 subjected to wind speed change from 12 m/s to 15 m/s(f) Active power transfer from Bus 3 to Bus 4 subjected to wind speed change from 12 m/s to 10 m/s(g) Active power transfer from Bus 5 to Bus 4 subjected to wind speed change from 12 m/s to 15 m/s(h) Active power transfer from Bus 5 to Bus 4 subjected to wind speed change from 12 m/s to 10 m/s
50
100
150
200
(a)
No SmartParks
SmartPark with SP-DC
SmartPark with SmartPark with IMFC_1' and IMFC_2'
176
178
180
182
150
200
250
300
(b)
178
179
180
181
50
100
150
Active p
ow
er(
MW
)
(c)
76
77
78
79
0
50
100
(d)
76
77
78
79
140
160
180
200
(e)
181
182
183
184
180
200
220
240
(f)
182
182.5
183
183.5
0 10 2010
20
30
40
(g)
0 10 2029
29.5
30
30.5
Time (s)
0 10 2020
40
60
(h)
0 10 2029.5
30
30.5
122
8.6 Summary
With the increased use of PEVs in power systems, the SmartPark can be applied for power
system control through charging and discharging of the PEV batteries. By injection of active and
reactive power at certain buses, SmartPark is able to impact the power flow in the power system,
leading to different operating conditions. With the application of PMUs, remote measurements in
power systems can be used for control purposes. To realize functionalities of SmartPark as
damping controller, voltage regulator, and active power transmission regulator simultaneously, the
proposed controller in this study is with two control loops: the inner control loop traces a reference
of active and reactive power references through current control of power electronic devices, while
Tagaki-Sugeno type fuzzy logic based IMFCs controllers generate the SmartPark active and
reactive power references using remote measurements. The parameters of IMFCs are heuristically
tuned using MVO. Simulation results have verified that the proposed controller is able to realize
the multiple functionalities of SmartParks.
As part of future work, concurrent realization of multiple functionalities of SmartPark in power
system control will be further tested and illustrated in multi-area power systems. In those cases,
the local, intra-area and inter-area oscillations appear in multiple modes [70]. Thus, more delicate
choices of input- , output-signals and objective functions will be essential. Due to the large
geographical size of power systems, a novel approach to optimally choose the site of SmartPark
installations will also be devised.
123
CHAPTER 9
CONCLUSION
9.1 Introduction
The previous chapters in this dissertation include: power system modeling and modal
analysis, development of local power system stabilizers and wide area signal based damping
controllers, application of SmartPark in power system stability control. This chapter serves as a
summary of the accomplishments in this dissertation.
9.2 Research summary
The research work presented in each chapter is summarized as follows:
Chapter 1: The concept of power stability is introduced. The Benchmark power
systems are presented. Main objectives and contributions of this dissertation are
enumerated.
Chapter 2: The phenomenon of power system oscillation is reviewed. The cause of
oscillation elaborated. The relationship between active power transfer and power
system oscillation is presented.
Chapter 3: Power system model is obtained through stochastic subspace
identification. Based on the system matrices, modal analysis is carried out for power
system oscillation
Chapter 4: Robust local power system stabilizers are developed using linear matrix
inequality based on power system matrices.
124
Chapter 5: Coherency analysis of generators is carried out using hierarchical
clustering and k-harmonic harmonic means clustering algorithms. The concept of
virtual generator is introduced.
Chapter 6: Virtual generator based power system stabilizer is developed to damp the
inter-area oscillations in multi-machine power systems.
Chapter 7: Artificial immune system is applied to realize adaptive wide area
measurement based power system stabilizers for better damping effectiveness under
various operating conditions.
Chapter 8: SmartParks are applied in power system with wind power integration to
realize the functionalities of damping controller, active power flow regulator and
voltage regulator concurrently.
9.3 Main conclusions
With the increase of load and the integration of renewable energy, power system is constantly
pushed toward stability margin, characterized by oscillations resulted from lack of damping torque.
The oscillation involves generators and transmission lines in the whole power system, as reflected
by fluctuating generator speeds, phase angles, power flows, and bus voltages. There are multiple
modes of oscillations characterized by different frequencies and damping ratios. They can be
categorized into local modes, intra-area modes, and inter area modes. For analysis of oscillation
modes, modal analysis can be carried out based on the system matrices identified using Stochastic
Subspace Identification (SSI). Through modal analysis, the oscillation modes in a power system
can be identified; moreover, the observability factor and controllability factor can be calculated as
a reflection of the relationship between the modes and generators.
125
The local modes and intra-area modes of oscillations can be damped by local Power System
Stabilizers developed using Linear Matrix Inequality (LMI) approach. For the inter-area modes,
since local measurements may lack observability for the oscillations in concern, wide-area
measurement based damping controllers can be used. During power system transients, generators
with small electrical distance generally oscillate coherently; thus, generators in a power system
can be classified into coherent groups using Hierarchical Clustering (HC) or K-Harmonic Means
Clustering (KHMC) algorithms. Each group of generators can be equivalent to a Virtual Generator
(VG). Based on this, a Virtual Generator based Power System Stabilizer (VG-PSS) is proposed
that makes use of VG speed deviation to generate a control signal on the generator of maximum
controllability. The parameters of the VG is automatically tuned through Particle Swarm
Optimization (PSO).
With the change of power system operating conditions, the generator coherency is subjected
to variation. In order to alleviate the impact of coherency variation on the effectiveness of VG-
PSS, an Artificial Immune System (AIS) is adopted to impose a deviation of parameter change to
the VG-PSS during power system transients, leading to improved efficacy of damping control. The
parameters of the AIS are also configured using PSO.
Besides damping control schemes via supplementary signal of generator Automatic Voltage
Regulators (AVRs), the batteries of electrical vehicles can also be utilized for maintenance of
power system stability. As part of future studies, fuzzy logic based controllers will be utilized to
regulate the active and reactive power references for SmartParks, to achieve the functionality of
shock absorber, voltage regulator and damping controller concurrently and coordinately, making
the power system more resistant to changes of operating conditions such as wind speed variations.
126
As a summary, despite the fact that power systems are facing more challenges with the
development of society, power system stability can be improved with the application of modern
control technologies and artificial intelligences.
9.4 Suggestions for future research
Despite of the effectiveness shown by the proposed schemes of stability control, the
following improvements can be made as a continuation of the research in this dissertation.
The development of local power system stabilizers for different generators can be
coordinated to improve damping effectiveness.
The online synchronous generator coherency grouping can be applied to adaptively
select wide area signals to VG-PSSs.
Multiple VG-PSSs can be applied in a large power system for better damping
effectiveness. The scheme to coordinate the VG-PSSs can be studied, for example,
using fuzzy logic
Concurrent realization of multiple functionalities of SmartParks in power system
control needs to studied further for multi-area large power systems.
The optimal placement of large SmartParks in a multi-area power system can be
investigated.
Adaptive VG-PSSs can be coordinated with SmartParks to enhance power system
stability.
127
9.5 Summary
A summary of the research work in this dissertation has been presented in this chapter. The
main conclusions have been presented. Suggestions for further research along the lines of
objectives of this dissertation have been highlighted.
128
APPENDIX A
IEEE 68-BUS SYSTEM GENERATION DATA
Table A.1 The reference of generator active power for VG-PSS design
Generator Active Power Generation for Base Condition
(MW)
Active Power Generation for
Operating Condition II
(MW)
Active Power Generation for
Operating Condition III.A
(MW)
Active Power Generation for
Operating Condition III.B
(MW)
Active Power Generation for
Operating Condition IV(MW)
G1 250 272.2 276.7 276.7 279.4
G2 545 567.2 571.7 571.7 574.4
G3 650 672.2 676.7 676.7 679.4
G4 632 654.2 658.7 658.7 661.4
G5 505.2 527.4 531.9 531.9 534.6
G6 700 722.2 726.7 726.7 729.4
G7 560 582.2 586.7 586.7 589.4
G8 540 562.2 566.7 566.7 569.4
G9 800 822.2 826.7 826.7 829.4
G10 500 500 500 500 500
G11 1150 1150 1150 1150 1150
129
Table A.2 The reference of generator active power development of adaptive wide area signal based PSS
Generator Base Case (MW) OC 1 (MW) OC 2 (MW) OC 3 (MW)
G1 250 279.4 281.1 283.3
G2 545 574.4 576.1 578.3
G3 650 679.4 681.1 683.3
G4 632 661.4 663.1 665.3
G5 505.2 534.6 536.3 538.5
G6 700 729.4 731.1 733.3
G7 560 589.4 591.1 593.3
G8 540 569.4 571.1 573.3
G9 800 829.4 831.1 833.3
G10 500 500 500 500
G11 1150 1150 1150 1150
G12 1350 1350 1350 1350
G13 3445 3180 3165 3595
G14 1785 1785 1785 1785
G15 1000 1000 1000 1000
G16 4000 4000 4000 4000
130
REFERENCES
[1] D. Molina, G. K. Venayagamoorthy, J. Liang and R. G. Harley, “Intelligent local area signals
based damping of power system oscillations using virtual generators and approximate
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BIOGRAPHY
Ke Tang, Clemson University
He received his MS degree from Chinese Academy of Sciences at 2012. He received his
Bachelor degree from Huazhong University of Science and Technology, Wuhan, China, in 2009.
His research emphasis is on modern power system stability and control including generator
coherency analysis, wide area signals based damping control, and stability issues with increasing
levels of renewable energy sources, and energy storage systems. He has been a Graduate Research
Asisstant with the Real-Time Power and Intelligent Systems Laboratory for the period August
2012 to April 2016. Ke received the third best student paper award at the 2016 IEEE Clemson
University Power System Conference for his paper entitled “Virtual Generators based Damping
Controller for a Multimachine Power System Using µ-Synthesis”.